In this paper we identify two counteracting effects of credit access on productivity growth: on the one hand, better access to credit makes it easier for entrepreneurs to innovate; on the other hand, better credit access allows less efficient incumbent firms to remain longer on the market, thereby discouraging entry of new and potentially more efficient innovators. We first develop a simple model of firm dynamics and innovation-base growth with credit constraints, where the above two counteracting effects generate an inverted-U relationship between credit access and productivity growth. Then we testour theory on a comprehensive French manufacturing firm-level dataset. We first show evidence of an inverted-U relationship between credit constraints and productivity growth when we aggregate our data at sectoral level.. We then move to firm-level analysis, and show that incumbent firms with easier access to credit experience higher productivity growth, but that they also experienced lower exit rates, particularly the least productive firms among them. To confirm our results, we exploit the 2012 Eurosystem's Additional Credit Claims (ACC) program as a quasi-experiment that generated exogenous extra supply of credits for a subset of incumbent firms.