While creating and running new ventures, entrepreneurs are exposed to conditions known to generate high levels of stress (e.g., rapid change, unpredictable environments, work overload, personal responsibility for others). Thus, it has been assumed that they often experience intense stress. A markedly different possibility, however, is suggested by Attraction-Selection-Attrition (ASA) theory. This perspective suggests that persons who are attracted by, selected into, and persist in entrepreneurship may be relatively high in the capacity to tolerate or effectively manage stress. In contrast, persons who are relatively low in this capacity tend to exit from entrepreneurship either voluntarily or involuntarily. As a result, founding entrepreneurs as a group are predicted to experience low rather than high levels of stress while running new ventures. Results supported this reasoning: Founding entrepreneurs reported lower levels of stress when compared to participants in a large national survey of perceived stress. Additional findings indicate that entrepreneurs’ relatively low levels of stress derive, at least in part, from high levels of psychological capital (a combination of self-efficacy, optimism, hope, and resilience). Psychological capital was negatively related to stress, and stress, in turn, was negatively related to entrepreneurs’ subjective well-being. Furthermore, and also consistent with ASA theory, the stress-reducing effects of psychological capital were stronger for older than younger entrepreneurs.