Gemara

(Mishnah): We read the Megilah on the 15th.

Question: R. Chelbo taught that everyone is Yotzei on the 14th, which is the time for all to read!

Answer: (The Mishnah teaches also other Mitzvos that apply on Adar 15.) It mentions the Megilah to teach that in a leap year, these Mitzvos apply only in Adar 2, just like Megilah. (It does not teach about whether one must read on the 14th or 15th - Taklin Chadtin.)

Question (R. Acha): It was taught that where the custom is to read on both days [due to a Safek], we do so! (According to R. Chelbo, in any case one was already Yotzei!)

Answer (R. Mana): Surely, a Ben Krach (walled city resident) who read on the 14th may [and should] read again on the 15th;

If he would not, the enactment that Kerachim read on the 15th would be uprooted!

Megilah 5b: Chizkiyah read the Megilah in Teverya on both days.

One 'wall' of Teverya is the sea. Chizkiyah was unsure if this suffices;

Perhaps it depends on whether or not the city is exposed. (Teverya is exposed);

Or, perhaps it depends on whether or not the city is protected. (Teverya is protected.)

Rav Asi read the Megilah on both days in Hutzal. He did not know whether it was walled from the days of Yehoshua.

Rishonim

Rambam (Hilchos Megilah 1:11): If there is a Safek whether a city was surrounded by a wall from the days of Yehoshua, or if it was surrounded afterwards, they read on both days and nights, i.e. 14th and 15th. They bless on the 14th, since it is the time to read for most of the world.

Magid Mishneh: Some say that it was Midas Chasidus to read on both days in Teverya and Hutzal, for letter of the law we follow the majority of cities, which were not surrounded [from the days of Yehoshua]. Some are stringent about the Safek only in Eretz Yisrael, for its cities were known at the time of the enactment, due to the law of Bayis Ir Chomah. In Chutz la'Aretz, it was enacted that whenever it is a Safek, they read only on the 14th. Some say that they held like the Rambam. It is proper to do so.

Ran (DH Megilah 2a DH ul'Inyan): If there is a Safek whether or not a city was surrounded from the days of Yehoshua, the Ge'onim follow the majority of cities, which were not surrounded, and they read on the 14th. Even if you will say that it is an even Safek, we are lenient about a Safek mid'Rabanan, so they are exempt on both days, and we would be Mevatel them from Keri'as ha'Megilah! Therefore, they read on the first day, and are exempt on the second. In Teverya and Hutzal, they read on both days. This was Midas Chasidus. In Teverya, the Safek was whether it depends on protection or exposure. In Hutzal there were different opinions about the tradition, whether or not it was surrounded from the days of Yehoshua. They read without a Berachah, for one need not bless on a Safek mid'Rabanan, like it says in Shabbos (23a). However, they bless on the 14th, like the majority of the world. The Rambam says that they read on both days and nights, but bless only on the 14th, since most of the world reads then.

Poskim

Shulchan Aruch (OC 688:4): If there is a Safek whether or not the wall around a city was from the days of Yehoshua, they read on the 14th and 15th and the nights. They bless only on the 14th, since it is the time to read for most of the world

Beis Yosef (DH v'Ra'isi): I saw that Ri Aviyuv denounced the custom to read on the 14th and 15th in every city surrounded by a wall. The Rambam said so only in a city which is a Safek, for some say that the wall is from the days of Yehoshua, and others disagree. If we do not know at all, this is not called a Safek. He brought a proof from the Rambam (Hilchos Shegagos 8:2), who obligates Asham Taluy only if there was an Isur Kavu'a, but not if there was only one piece of Safek Chelev, Safek [permitted] lard. We can learn from there to Kri'as ha'Megilah. If nothing suggests that a city was surrounded [from the days of Yehoshua, we read only on the 14th.

Beis Yosef (DH v'Li): I disagree with his proof. If so, we should say so even if they argue about a tradition! One is exempt from Asham Taluy in such a case. If so, when does the Rambam obligate reading on both days? Also, we learn about Asham Taluy from "mi'Kol Mitzvos" (Kerisus 17b). A Gezeras ha'Kasuv exempts, but not because it is not a Safek. However, the Ran supports Ri Aviyuv. He connotes that it was a Safek only due to different traditions. It seems that the custom to read on both days in every walled city is because we see that it has a wall, so it is considered a Safek, which the Rambam says reads on both days. I later saw that Maharal (56) asked why we do not read also on the 15th. How do we know that there was not a wall from the days of Yehoshua? He answers that we assume that there was not a wall, unless we know that there was, or know of a reason for a Safek.

Taz (4): Maharshal asked why we do not bless on both days, like other Sefekos about the day. It is difficult to distinguish between Yom Tov mid'Oraisa and Megilah mid'Rabanan. The Mordechai answered why we do not read on both days due to the Safek which day was fixed to be Rosh Chodesh. It says "v'Lo Ya'avor" (we do not pass over the day to read). We [have a fixed calendar, and] know which day was Rosh Chodesh. This does not apply to a Safek about which day we should read on! We should bless on both days, just like we bless on both days of Yom Tov! We can distinguish. Kedushas Yom Tov obligates blessing due to Safek. If we will not conduct with Kedushah also regarding Berachah, we treat the day like Chol. Also, Kedushas ha'Yom depends on Beis Din. This is how they accepted [to fix the calendar].

Rebuttal (Taz): Also regarding Megilah, there is Kedushah to the day, for all laws of Purim! Why didn't Beis Din enact Megilah similar to Yom Tov? I answer that regarding Yom Tov, if we consider only one day Kodesh, perhaps it was the wrong day, and we did not fulfill Yom Tov at all! Therefore, we must observe both days. We expound that many days were enacted for Kri'as ha'Megilah (11,12, 13). Also where they read on the 15th, sometimes we read early, e.g. when the 15th is on Shabbos. The Beis Yosef brings from the Yerushalmi that the entire month until the 15th is Kosher for the Megilah. Therefore, even if the 15th is primary, it suffices to read on the 14th.

Magen Avraham (4): The Shlah says that there are cities in Chutz la'Aretz about which there is a Safek. The Levush says that there is no Safek in our lands, which are in the north and far from Eretz Yisrael, and it is known that they were not settled in the days of Yehoshua.

Magen Avraham (5): They have Simchah and Matanos l'Evyonim on both days.

Magen Avraham (6): We bless on both days only when Chachamim enacted to do [e.g. two days of Yom Tov] due to Safek. We do not bless when we [ourselves] do due to Safek, even for a Safek mid'Oraisa (YD 28:3, 20, Rema 28:4, regarding Kisuy ha'Dam).

Gra (DH Krach): The Magid Mishneh and Ran say that one is Yotzei b'Di'eved on the 14th. This is why the Rambam says that we bless only on the 14th.

Gra (DH v'Lo): The Rif (Shabbos 54a) in the name of Rav Hai Gaon, the Rosh (Shabbos 19:5) and Rivash (221) say that we do not bless even on a Safek mid'Oraisa. They explain that Shabbos 23a teaches that we bless on a Vadai mid'Rabanan, but not if it was enacted due to a Safek, such as Demai. Rava disagrees. Since they enacted, even due to Safek, one must bless. We do not bless for other Sefekos, even mid'Oraisa, like we say about Milah and [Kisuy ha'Dam of] a Safek Chayah. Teshuvas ha'Rambam brings a proof from Sukah 47a. We sit in the Sukah on Shemini Atzeres [in Chutz la'Aretz, due to Safek], but do not bless. This is because the Berachah is mid'Rabanan, even for Torah Mitzvos. The Rosh brings from R. Yonah that Rava exempts Demai only because most Amei ha'Aretz tithe. We bless on any Torah Safek, e.g. Yom Tov Sheni, even if it was not an enactment. One who reads Keri'as Shema due to Safek does not bless, for it (the Berachah) is mid'Rabanan. Sukah is different, for it is contradictory [to bless on Yom Tov and on the Sukah]. The Shulchan Aruch rules like Rif, Rambam and Rosh. The Rambam in Hilchos Chanukah 3:6 retracted from what he wrote in the Teshuvah. There he says that Rava does not argue with Abaye. He merely adds that we do not bless even for a Takanah due to a Safek Torah. All agree that we do not bless for a Takanah due to a Safek mid'Rabanan.

Gra (DH Ki): The Yerushalmi says that a Ben Krach can be Motzi a Ben Ir, but not vice-versa, for all are Yotzei on the 14th. This is like a Safek Borei Peri ha'Etz, Safek Borei Peri ha'Adamah. (We say the latter, for in any case he is Yotzei with it.)

Mishnah Berurah (15): In Teverya they must read on both days.

Kaf ha'Chayim (15): Since Mordechai and Esther were not stringent for the Safek of which day was Rosh Chodesh, Chachamim were not stringent for it. Also, the entire month was transformed to Simchah. Also, it was enacted [on the 14th] so people [who count 30 days from Purim to Pesach] will not eat Chametz during Pesach.

Kaf ha'Chayim (17,19): The custom in Chevron and Tzefas is to read on the 14th and 15th. Some say that this is the custom in all cities of Eretz Yisrael, except for Yerushalayim, which reads only on the 15th.

Kaf ha'Chayim (23): In Tzefas, the Ari Zal did not say Al ha'Nisim in Shemoneh Esre on the 15th, nor did R. Chaim Vital in Dameshek, for it is a Safek Hefsek.