Online marketplaces have reduced entry costs across a variety of industries. These marketplaces allow small and part-time service providers (peers) to participate in economic exchange. For example, Airbnb allows anyone to become a hotelier and Uber allows anyone to become a cab driver. The entry of peer-to-peer competitors has two effects: market expansion and business stealing. The first effect occurs when the peer-to-peer sector supplies price sensitive or niche consumers who were previously underserved. The second effect occurs when the peer-to-peer sector attracts consumers away from conventional suppliers. We study these two effects using data from the hotel industry and Airbnb. We show that the market expansion and business stealing effects differ by location, and attribute this heterogeneity to supply constraints - legal and geographic - relative to the level of demand. We then derive a simple model of competition between a peer-to-peer marketplace and hotels to explain these findings. In the model, hotels and peer-to-peer suppliers differ in their fixed (higher for hotels) and marginal costs (higher for peer-to-peer suppliers). The model allows us to study how the efficient market structure depends on the level and variability of demand, and to quantify the welfare gains from peer-to-peer entry in the accommodation industry.