It's an ugly little open secret that Arkansas, Maryland, Mississippi, North Carolina, South Carolina, Tennessee and Texas have constitutions that explicitly forbid atheists from holding state office.
These laws are archaic and unenforceable in principle -- they were all ruled unconstitutional in 1961 -- but of course they're still in effect across all 50 states in practice, since public opinion makes it almost impossible for an atheist to get elected to high office.
Now, though, a representative in Arkansas has submitted a bill to amend the Arkansas constitution and remove the prohibition of atheists. This could get very interesting, or it might not. If the Arkansas legislature does the sensible thing and simply and efficiently removes an old law that can't be enforced anyway, I will be pleased, but there won't be much drama.