We introduce immigration into an overlapping-generations growth model. A planner chooses the rate of immigration to maximize the utility of a representative native consumer in the steady state, subject to providing each immigrant with a threshold level of utility. We derive a sufficient condition for the optimal immigration rate to be positive, identifying the components of the marginal cost and marginal benefit of immigration. The planner's optimal steady state can be implemented in a competitive economy using a fiscal package consisting of an entry fee for immigrants, a consumption tax, and government bonds.