Equal pay laws increasingly require that workers with different group identities doing ``similar'' work are paid equal wages within firm. We study such ``equal pay for similar work'' (EPSW) policies theoretically and test our models' predictions empirically using evidence from a 2009 gender-based Chilean EPSW. Under EPSW, firms segregate their workforce by gender. When there are more men than women in a labor market, EPSW increases the gender wage gap.