Gender differences in competitive behavior have been well documented by economists and other social scientists; however, the bulk of the research addresses competition with others and excludes other economically relevant competition that may contribute to the gender pay gap. In this paper, we ask: How does gender affect how individuals react to competition against themselves? In a laboratory experiment in which some subjects compete against others and some compete against themselves, we find women select into intrapersonal competition at significantly higher rates than interpersonal competition, the first such findings. We find perseverance or "grit" to be a poor predictor of interpersonal competition selection, but find familial effects such as parent's education and number of brothers to be correlated with competition selection.