Recent empirical findings indicate that when trade is liberalized both firm selection takes place and product variety increases. Each of these two stylized facts has its own seminal theory. But how can they arise together? This paper presents a model of heterogeneous, multi-variety firms that provides an intuitive explanation. When trade is liberalized efficient foreign exporters enter and push out the least efficient domestic firms. Fewer firms remain in total. But exporters endogenously offer more variety than domestic firms. The entry of variety-rich foreign firms unambiguously dominates the decrease in the number of firms. Thus, total variety increases. Copyright � 2010 Blackwell Publishing Ltd.