From the Illinois Department of Public Health:

Generally, marriages between cousins of the first degree are prohibited; however, first cousins may marry if --

• both parties are 50 years of age or older; or
• either party, at the time the couple applies for a marriage license, presents to the county clerk of the county in which the marriage is to take place a certificate signed by a licensed physician stating that the party to the proposed marriage is permanently and irreversibly sterile.

Illinois is going to great lengths to prevent cousins from procreating, and yet allow cousins to be legally married. Isn't this silly? Why go to so much trouble?

Man: Hi. We'd like to get a marriage license.
County Clerk: Yes sir. Are you cousins?
Woman: Yes, but I am unable to have children.
County Clerk: How do you know that?
Woman: Oh, we've been trying to have children for several years now, but have been unsuccessful. We finally went to a fertility specialist, and she said I was infertile.
Man: So then we thought, "Hey! Since we can't have any kids, we might as well get married."
County Clerk: Swell.