Question:

When the Jewish People conquered the land, the tribe of Levi did not receive an inheritance. Will this also be the case in the Messianic era?

Answer: 

With the future Redemption, the Levites will be allowed to take an inheritance on the Eastern bank of the Jordan, and evidently, on the Western bank as well.

There is a difference of opinion regarding the status of the tribe of Levi in the Messianic era. According to a verse in the book of Ezekiel, there will be "one gate of Levi" amongst the tribes. Some conclude from this verse that the tribe of Levi will receive an inheritance among the tribes. (This is the view that the Lubavitcher Rebbe is inclined to accept, since the many of the differences between the Levites and the other tribes will be removed when Moshiach comes.)

Others interpret the verse to mean that each tribe will set aside land from its own portion for Levites, but the Levites themselves will not have their own land.

Maimonides offers a third view: The restriction on the tribe of Levi inheriting land applies only to the land of Canaan, which was promised to Abraham, Isaac and Jacob and was conquered by their descendants. But any other lands that will later be conquered by kings of Israel will be divided up among all the tribes, including Levi.

In addition to the land of Canaan, there are three other lands, the Keini, Knizi and Kadmoni, which were promised to Abraham but not conquered by his children. Apparently, the tribe of Levi will also be able to receive an inheritance in these lands, since they are outside the borders of Canaan.

It follows, then, that Levites have an especial reason to anticipate the Redemption: They will finally merit receiving a portion in the land promised by G-d.