This paper explores the extent to which "zombie" firms - defined as old firms that have persistent problems meeting their interest payments - are stifling labour productivity performance. The results show that the prevalence of and resources sunk in zombie firms have risen since the mid-2000s and that the increasing survival of these low productivity firms at the margins of exit congests markets and constrains the growth of more productive firms. Controlling for cyclical effects, cross-country analysis shows that within-industries over the period 2003-2013, a higher share of industry capital sunk in zombie firms is associated with lower investment and employment growth of the typical non-zombie firm and less productivity-enhancing capital reallocation. Besides limiting the expansion possibilities of healthy incumbent firms, market congestion generated by zombie firms can also create barriers to entry and constrain the post-entry growth of young firms. Finally, we link the rise of zombie firms to the decline in OECD potential output growth through two key channels: business investment and multi-factor productivity growth