In this paper we present results relating undergraduate student retention in science, technology, engineering, and mathematics (STEM) majors to the use of Peer Instruction (PI) in an introductory physics course at a highly selective research institution. We compare the percentages of students who switch out of a STEM major after taking a physics course taught using traditional lectures only or one taught using PI, finding that nearly twice the percentage of students switch after the lecture-based course. By examining these results in light of the literature on STEM retention, we propose that providing opportunities for students to think, respond, and interact in class may have a substantial impact on the retention of students in STEM disciplines. (Contains 1 table and 3 figures.)