We report the discovery of an eclipsing cataclysmic variable with eclipse depths > 5.7 mag, orbital period 94.657 minutes, and peak brightness V similar to 18 at J2000 position 17(h)25(m)54(s). 8, -64 degrees 38'39 ''. Detected by visual inspection of images from Yale University's QUEST camera on the European Southern Observatory 1.0 m Schmidt telescope at La Silla, we obtained light curves in B, V, R, I, z, and J with SMARTS 1.3 m and 1.0 m telescopes at Cerro Tololo and spectra from 3500 to 9000 angstrom with the SOAR 4.3 m telescope at Cerro Pachon. The optical light curves show a deep, 5-minute eclipse immediately followed by a shallow 38-minute eclipse and then sinusoidal variation. No eclipses appear in J. During the deep eclipse we measure V-J > 7.1, corresponding to a spectral type M8 or later secondary, consistent with the dynamical constraints. The estimated distance is 150 ps. The spectra show strong hydrogen emission lines, Doppler broadened by 600-1300 km s(-1), oscillating with radial velocity that peaks at mid deep eclipse with semi-amplitude 500 +/- 22 km s(-1). We suggest that LSQ172554.8-643839 is a polar with a low-mass secondary viewed at high inclination. No known radio or X-ray source coincides with the new object's location.