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We report on XMM-Newton X-ray observations that reveal CTCV J2056-3014 to be an unusual accretion-powered, intermediate polar (IP) system. It is a member of the class of X-ray-faint IPs whose space density remains unconstrained but potentially very high, with L(sub χ,0.3-12 keV of 1.8 × 10(exp 31) erg s(exp -1). We discovered a coherent 29.6 s pulsation in X-rays that was also revealed in our reanalysis of published optical data, showing that the system harbors the fastest-spinning, securely known white dwarf (WD) so far. There is no substantial X-ray absorption in the system. Accretion occurs at a modest rate (∼6 × 10(exp -12)M(sub ⨀) yr(exp -1) in a tall shock above the WD, while the star seems to be spinning in equilibrium and to have low magnetic fields. Further studies of CTCV J2056-3014 potentially have broad implications on the origin of magnetic fields in WDs, on the population and evolution of magnetic cataclysmic variables, and also on the physics of matter around rapidly rotating magnetic WDs.