We present the results of Chandra X-ray Observatory ( CXO ) observations of the planetary nebulae ( PNs ) NGC 40 and Hen 2-99 . Both PNs feature late-type Wolf-Rayet central stars that are presently driving fast ( \sim 1000 km s ^ { -1 } ) , massive winds into denser , slow-moving ( \sim 10 km s ^ { -1 } ) material ejected during recently terminated asymptotic giant branch ( AGB ) evolutionary phases . Hence , these observations provide key tests of models of wind-wind interactions in PNs . In NGC 40 , we detect faint , diffuse X-ray emission distributed within a partial annulus that lies nested within a \sim 40 ^ { \prime \prime } diameter ring of nebulosity observed in optical and near-infrared images . Hen 2-99 is undetected . The inferred X-ray temperature ( T _ { X } \sim 10 ^ { 6 } K ) and luminosity ( L _ { X } \sim 2 \times 10 ^ { 30 } ergs s ^ { -1 } ) of NGC 40 are the lowest measured thus far for any PN displaying diffuse X-ray emission . These results , combined with the ring-like morphology of the X-ray emission from NGC 40 , suggest that its X-ray emission arises from a “ hot bubble ” that is highly evolved and is generated by a shocked , quasi-spherical fast wind from the central star , as opposed to AGB or post-AGB jet activity . In constrast , the lack of detectable X-ray emission from Hen 2-99 suggests that this PN has yet to enter a phase of strong wind-wind shocks .