I estimate the impact of market-rate new housing supply on the local rent distribution. As an exogenous shifter of new housing supply, I exploit local weather shocks during the construction phase that lead to temporary delays in housing completions at the municipal level. Adding one new housing unit to the stock for every 100 rental housing units offered on the market in a given month reduces rents by 0.4-0.7%. A series of instrumental variable quantile regressions show that shocks to new housing supply shift the rent distribution as a whole, suggesting that market-rate new housing supply effectively reduces housing costs of all renter households. I rationalize this finding by analyzing moving decisions in the German Socio-Economic Panel. The housing quality at a household's previous address is a poor predictor of the housing quality at the current address, suggesting that new housing supply triggers supply of (rental) housing units across the housing quality spectrum.