Equal pay laws increasingly require that workers doing "similar" work are paid equal wages within firm. We study such "equal pay for similar work" (EPSW) policies theoretically and test our model's predictions empirically using evidence from a 2009 Chilean EPSW. When EPSW only binds across protected class (e.g., no woman can be paid less than any similar man, and vice versa), firms segregate their workforce by gender. When there are more men than women in a labor market, EPSW increases the gender wage gap. By contrast, EPSW that is not based on protected class can decrease the gender wage gap.