Close binary systems undergoing mass transfer or common envelope interactions can account for the morphological properties of some planetary nebulae. The search for close binary companions in planetary nebulae is hindered by the difficulty of detecting cool, late-type, main-sequence companions in binary systems with hot pre-white-dwarf primaries. However, models of binary planetary nebula progenitor systems predict that mass accretion or tidal interactions can induce rapid rotation in the companion, leading to X-ray-emitting coronae. To test such models, we have searched for, and detected, X-ray emission from three binary central stars within planetary nebulae: the postcommon envelope close binaries in HFG 1 and DS 1 consisting of O-type subdwarfs with late-type, main-sequence companions and the binary system in LoTr 5 consisting of O-type subdwarf and rapidly rotating, late-type giant companion. The X-ray emission in each case is best characterized by spectral models consisting of two optically thin thermal plasma components with characteristic temperatures of ~10 MK and 15-40 MK and total X-ray luminosities ~1030 erg s-1. We consider the possible origin of the X-ray emission from these binary systems and conclude that the most likely origin is, in each case, a corona around the late-type companion, as predicted by models of interacting binaries.