We present a theoretical explanation of the gender wage gap which turns on the interaction between men and women in households. In equilibria where men are over-represented in full-time work, we show that firms rationally choose to hire women only at strictly lower wages than men. The model developed predicts a gap even controlling for education, occupation and industry of workers and does so in a competitive labor market where there exist no inherent gender differences. We test our theory using CPS data over the period 1979-98 and find it is strongly supported by the data.