The lawsuit accuses city officials of failing to obey a federal court ruling that the plaza is a public forum.
The ACLU, in its legal filing, said Salt Lake officials "acquiesced to the demands of the (Mormon) Church and created a powerful platform for the church to promulgate its message on a range of social, political and religious issues, while prohibiting others from sharing their own messages on the same issues in the same place and in the same manner."
At issue is a block of Main Street that Salt Lake City sold to the Church of Jesus Christ of Latter-day Saints in 1999. The church subsequently placed restrictions on people's speech and behaviors on the plaza. The restrictions were struck down last year by a federal appeals court.