KIC 9406652 is a remarkable variable star in the Kepler field of view that shows both very rapid oscillations and long term outbursts in its light curve. We present an analysis of the light curve over quarters 1 to 15 and new spectroscopy that indicates that the object is a cataclysmic variable with an orbital period of 6.108 hours. However, an even stronger signal appears in the light curve periodogram for a shorter period of 5.753 hours, and we argue that this corresponds to the modulation of flux from the hot spot region in a tilted, precessing disk surrounding the white dwarf star. We present a preliminary orbital solution from radial velocity measurements of features from the accretion disk and the photosphere of the companion. We use a Doppler tomography algorithm to reconstruct the disk and companion spectra, and we also consider how these components contribute to the object's spectral energy distribution from ultraviolet to infrared wavelengths. This target offers us a remarkable opportunity to investigate disk processes during the high mass transfer stage of evolution in cataclysmic variables. ; Comment: 31 pages, 13 figures, accepted for ApJ