We report on two years of photometric and spectroscopic observation of the recently discovered AM Herculis star RX J19402-1025. A sharp eclipse feature is present in the optical and X-ray light curves, repeating with a period of 12116.290±0.003 s. The out-of-eclipse optical waveform contains approximately equal contributions from a signal at the same period and another signal at 12150 s. As these signals drift in and out of phase, the wave form of the light curve changes in a complex but predictable manner. After one entire "supercycle" of 50 days (the beat period between the shorter periods), the light curve returns to its initial shape. We present long-term ephemerides for each of these periods. It is highly probable that the eclipse period is the underlying orbital period, while the magnetic white dwarf rotates with P = 12150 s. The eclipses appear to be eclipses of the white dwarf by the secondary star. But there is probably also a small obscuring effect from cold gas surrounding the secondary, especially on the orbit-leading side where the stream begins to fall towards the white dwarf. The latter hypothesis can account for several puzzling effects in this star, as well as the tendency among most AM Her stars for the sharp emission-line components to slightly precede the actual motion of the secondary. The presence of eclipses in an asynchronous AM Her star provides a marvelous opportunity to study how changes in the orientation of magnetic field lines affect the accretion flows. Repeated polarimetric light curves and high-resolution studies of the emission lines are now critical to exploit this potential. Leighly et al. 1993). Among active galactic nuclei, this was the only strictly periodic signal reported at any wavelength that passes tests of persistence and phase stability. It has been difficult to understand this behavior. Madejski et al. (1993) have ended the mystery by showing that, although the period is indeed real, it belongs not to NGC 6814 but to another X-ray source 37 arcmin away in the sky. Follow-up spectroscopy and photometry of several stars in the smaller X-ray error circle revealed the nature of the interloper: a cataclysmic variable, almost certainly of the AM Herculis variety, and provisionally named RX J19402 -1025 (Madejski et al. 1993;Staubert et al. 1994; «2000= 19 h 40 m ll?6, <%ooo= -10°25'25'. '7).Although NGC 6814 is now relegated to obscurity, the new X-ray source will surely become one of the most-307