My school East Stroudsburg University (www.esu.edu) offers a Computer Security degree. From what they're researched and I've seen it's the only undergraduate program of it's kind in the country. I am currently double majoring in Comp Sci and Security.

In my opinion you must have a good understanding of programming to fully understand security. If you don't fully understand what is going on at the machine level, if you don't know how to read a memory dump, how the machine executes an instruction, etc -- then as much as you think you know about security, you will never fully understand it. Security is a complex and probably one of the hardest fields out there because in order to be a true expert you must have an understanding of how computers work from the ground up.