This paper provides the first evidence about pure exporters (i.e., firms exporting all of their output to the foreign market) -- a phenomenon overlooked and cannot be explained in the existing literature. It then offers a generalized model of Melitz (2003) for examining the existence and behavior of pure exporters. In particular, pure exporters arise when the export market is sufficiently large -- a situation more likely to hold in developing countries as opposed to large developed countries; and their productivity levels are above those of non-exporters, but below those of firms having both domestic sales and export. These theoretical predictions are borne out in a data of Chinese manufacturing firms for the period of 1998-2005