We study the local effects of new market-rate housing in low-income areas using microdata on large apartment buildings, rents, and migration. New buildings decrease nearby rents by 5 to 7 percent relative to locations slightly farther away or developed later, and they increase in-migration from low-income areas. Results are driven by a large supply effect - we show that new buildings absorb many high-income households - that overwhelms any offsetting endogenous amenity effect. The latter may be small because most new buildings go into already-changing areas. Contrary to common concerns, new buildings slow local rent increases rather than initiate or accelerate them.