Investment banking is very prestige-oriented. Your application will be in the shadow of the Columbia and Harvard kids, but I won't go so far as to call it impossible.
True story: I once went to a career workshop at Haverford College. The presenter was working for a Philadelphia-based investment bank. At the end of the presentation, a student asked him if his company had internships or entry-level positions for college students. His response: "Yes, but we hire exclusively from Princeton and Wharton."