This paper investigates whether physiological measures related to chronic and acute stress predict individual differences in willingness to compete. We measure individuals' autonomic nervous system activity in a resting state as well as under non-competitive and competitive incentive schemes using heart rate variability (HRV) measurement. We find that both baseline HRV and competition-induced changes in HRV predict willingness to compete. Notably, we find that women with low baseline HRV, a marker associated with chronic stress exposure, are more likely to choose piece rate incentives over competitive incentives than women with high baseline HRV. We observe that men with large acute HRV response to forced competition are more likely to choose tournament pay over piece rate pay than men with small acute HRV response to competition. Our results suggest that HRV can predict individual differences in willingness to compete, but HRV does not close the gender gap in willingness to compete at the aggregate level.