U.S. District Court Judge Richard Matsch hears arguments Wednesday, on a request to order Palmer High School to recognize a club that includes gay students.
Matsch has already held an evidentiary hearing in the case involving the Colorado Springs school.
The school district has said it does not recognize clubs that have no connection to curriculum.
But the American Civil Liberties Union, which is handling the case for the Gay-Straight Alliance, says the district has allowed clubs with no curriculum connection to operate.
The Gay-Straight Alliance was formed partly to allow a forum for dicussion of the treatment of gays and lesbians at the school.