The chapel for the 3rd Ward of the Church of Jesus Christ of Latter-day Saints.
It was located on 700 South between State Street and 200 East.
This comment Regina Andrus made on this page has some great info:
The Third Ward was an adobe building built by the early pioneers, the last chapel still standing in the 1950s in which Brigham Young had spoken from its pulpit. The pulpit and the choir seats were elevated with a tiny room was situated under the pulpit in which to store the sacrament trays, plus hand-held fans from the local Kingdon Mortuary as there was no air conditioning. Behind the adobe chapel, a large wooden 2-story structure was added which housed a coat room, the bishop’s office, and classrooms on the first floor. The second story held a gymnasium and a stage. A passage way linked the stairs to the stage so that performers could enter and exit unseen. The ward was a vibrant downtown ward through the 50s and into the 60s where most ward members lived within walking distance of a few blocks. With many people moving to the suburbs in the 60s, I believe the ward became a German-speaking ward and later a ward for Korean speakers. The wooden structure burned down at some point and the building was razed. The Church eventually built a Deseret Industries on that spot, which has now also been razed.