  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 ~1000 km/s, massive
winds into denser, slow-moving (~10 km/s) 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 ~40'' diameter ring of nebulosity observed in
optical and near-infrared images. Hen 2-99 is undetected. The inferred X-ray
temperature (T_X ~10^6 K) and luminosity (L_X ~ 2 X 10^30 ergs/s) 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.
