The National Science Foundation and others groups sponsors programs at many universities that allow undergraduate chemistry majors to be paid while performing undergraduate research.
NSF Summer Research Opportunities Page for Chemistry
For Research in Material Science (some programs are very chemistry oriented)
Search for a Wide Variety of Research/Experience Opportunities Here
Internships for Science and Engineering Majors
NC State University Summer Internship List for Science and Engineering
These sites are for many areas and have fewer applicable to chemistry
National Labs Intern and Summer Research Programs - If the link does not take you directly to the program site, find the link to educatinal programs or student programs.