This paper examines the impact of an export market expansion created by the US-Vietnam Bilateral Trade Agreement (BTA) on competition among manufacturing firms in Vietnam's local labor markets. Using a nonparametric production function approach, we measure distortionary wedges between equilibrium marginal revenue products of labor (MRPL) and wages. We find that the median manufacturing firm pays workers 59% of their MRPL. Following the BTA, which significantly reduced US import tariffs for Vietnamese products, firms in industries exposed more to the tariff reductions saw faster employment growth and faster declines in their MRPL-wage wedge. We find that the BTA permanently decreases labor market distortion in manufacturing by 3.4%, and the effect concentrates on domestic private firms with a magnitude of 4.9%. We exploit information on the gender composition to estimate the MRPL-wage wedges separately for men and women. We find that the median distortion is 26% higher for women relative to men, and the decline in distortion for women, amounting to more than 12%, is the driver of the overall reduction in labor market distortion attributable to the BTA. Our theory and empirics suggest that the entry of FDI firms combined with differential aggregate labor supply elasticities explains these results.