  KPD 0005+5106, with an effective temperature of $\simeq$200,000 K, is one of
the hottest white dwarfs (WDs). ROSAT unexpectedly detected "hard" ($\sim$1
keV) X-rays from this apparently single WD. We have obtained Chandra
observations that confirm the spatial coincidence of this hard X-ray source
with KPD 0005+5106. We have also obtained XMM-Newton observations of KPD
0005+5106, as well as PG 1159$-$035 and WD 0121$-$756, which are also
apparently single and whose hard X-rays were detected by ROSAT at
3$\sigma$-4$\sigma$ levels. The XMM-Newton spectra of the three WDs show
remarkably similar shapes that can be fitted by models including a blackbody
component for the stellar photospheric emission, a thermal plasma emission
component, and a power-law component. Their X-ray luminosities in the $0.6-3.0$
keV band range from $4\times10^{29}$ to $4\times10^{30}$ erg~s$^{-1}$. The
XMM-Newton EPIC-pn soft-band ($0.3-0.5$ keV) lightcurve of KPD 0005+5106 is
essentially constant, but the hard-band ($0.6-3.0$ keV) lightcurve shows
periodic variations. An analysis of the generalized Lomb-Scargle periodograms
for the XMM-Newton and Chandra hard-band lightcurves finds a convincing
modulation (false alarm probability of 0.41%) with a period of 4.7$\pm$0.3 hr.
Assuming that this period corresponds to a binary orbital period, the Roche
radii of three viable types of companion have been calculated: M9V star, T
brown dwarf, and Jupiter-like planet. Only the planet has a size larger than
its Roche radius, although the M9V star and T brown dwarf may be heated by the
WD and inflate past the Roche radius. Thus, all three types of companion may be
donors to fuel accretion-powered hard X-ray emission.
