An influential recent literature argues that women are less likely to initiate bargaining with their employers and are (often) less effective negotiators than men. We use longitudinal wage data from Portugal, matched to balance sheet information on employers, to measure the relative bargaining power of men and women and assess the impact of the gender gap in bargaining strength on the male-female wage gap. We show that a model with additive fixed effects for workers and gender-specific fixed effects for firms provides a close approximation to the wage structure for both men and women. Building on this model we present three complementary approaches to identifying the impact of differential bargaining strength. First, we perform a simple decomposition by assigning the firm-specific wage premiums for one gender to the other. Second, we relate the wage premiums for men and women to measures of employer profitability. Third, we show that changes in firm-specific profitability have a smaller effect on the wage growth of female than male employees. All three approaches suggest that women are paid only 85-90% of the premiums that men earn at more profitable firms. Overall, we estimate that the shortfall in women‘s relative bargaining power explains around 3 percentage points – or 10-15% – of the gender wage gap in Portugal.