We analyze entry of a firm with a new and differentiated product into a market with two properties: An existing incumbent has a captive consumer base, and all consumers have heterogeneous tastes. The interaction between the share of captive consumers and the degree of taste heterogeneity leads to nonmonotone effects of both parameters on entry: The captive share can have an inverse-U relation with entry profits, and higher taste heterogeneity (i.e., less product substitutability) can impede entry in the presence of captive consumers.