The trial is over a lawsuit seeking the removal of the 5,300-pound granite Ten Commandments Monument that sits in the lobby of the Alabama Judicial Building.
Legal experts said the case could eventually be the one the U.S. Supreme Court uses to decide if such monuments in and around government buildings are constitutional.
The monument was moved into the building in the middle of the night by Chief Justice Roy Moore.
It has two stone tablets containing the Commandments on a granite block. The monument also includes quotes from historical figures such as George Washington, Thomas Jefferson and James Madison.
The Southern Poverty Law Center and Americans United for Separation of Church and State asked U.S. District Judge Myron Thompson to order the monument removed.