According to their respective state constitutions, it is illegal for atheists to hold office in Arkansas, Maryland, Texas, Mississippi, Tennessee, and both Carolinas.
Surely these are dormant, outdated clauses, you say? Not so fast: in Asheville, North Carolina, enraged Christians are demanding that duly-elected council member Cecil Bothwell resign because he does not believe in God. They have the state law on their side. Article 6, section 8 of North Carolina's constitution says: "The following persons shall be disqualified for office: First, any person who shall deny the being of Almighty God."