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 $4times10^{29}$ to $4times10^{30}$ 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.
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