Q. When no Cohen is present in shul, and when other favoring factors such as being a greater Talmid Chacham or an elder are not applicable, does a Levi get preference for a first aliya? How about for leading in Birchat Hamazon?
A. Mishna Berura (201: 13) maintains that it is better to precede and give honor to a Levy before a Yisroel, when other factors are equal, not only regarding leading Birchas Hamazon or reciting hamotzi, but also in receiving a first aliya. Aruch Hashulchan (135: 12) rules similarly quoting Rosh, since the posuk (Devarim 10: 8) mentions that Hashem separated the tribe of Levi to bear the ark of the covenant and, to stand before Hashem to serve Him, and to bless in His Name, to this day. (See Kovetz Shiurim – Baba Basra 277 that presents a dissenting view).
Horav Shlomo Miller’s Shlit’a opinion is similar to the Mishna Berura. The Rov also quoted the Talmud Horios (13a).
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a