Here's a web page that lists four places in the U.S. that offer chess scholarships: http://www.kirshnerisms.com/GomesChess/Scholarships.html The four colleges are the University of Maryland, Baltimore County; Manhattan Community College; the University of Texas, Dallas; and Kenyon College. It's not impossible that there are a few other places, but there certainly aren't many.

You should approach Chess Organisations such as FIDE instead. It is unlikely that universities will give you scholarships for chess. ~ It is likely that Chess can be an extra-curricular bonus to aid you in getting into the university. But i do not think there would be scholarships for it. ~ Alas, I do not live in America, so I cannot answer you in the definitive. You could try calling the Office of Admissions of the various universities to ask about it.

Since I'm only average at chess, my guess is none.