We report a photometric and spectroscopic study of the peculiar cataclysmic variable SDSS 1507+52 . The star shows very deep eclipses on the 67 minute orbital period , and those eclipses are easily separable into white-dwarf and hot-spot components . This leads to tight constraints on binary parameters , with M _ { 1 } = 0.83 ( 8 ) M _ { \odot } , M _ { 2 } = 0.057 ( 8 ) M _ { \odot } , R _ { 1 } = 0.0097 ( 9 ) R _ { \odot } , R _ { 2 } = 0.097 ( 4 ) R _ { \odot } , q = 0.069 ( 2 ) , and i = 83.18 ( 13 ) degrees . Such numbers suggest possible membership among the WZ Sge stars , a common type of dwarf nova . The spectroscopic behavior ( strong and broad H emission , double-peaked and showing a classic rotational disturbance during eclipse ) is also typical . But the star ’ s orbital period is shockingly below the “ period minimum ” of \sim 77 min which is characteristic of hydrogen-rich CVs ; producing such a strange binary will require some tinkering with the theory of cataclysmic-variable evolution . The proper motion is also remarkably high for a star of its distance , which we estimate from photometry and trigonometric parallax as 230 \pm 40 pc . This suggests a transverse velocity of 164 \pm 30 km/s - uncomfortably high if the star belongs to a Galactic-disk population . These difficulties with understanding its evolution and space velocity can be solved if the star belongs to a Galactic-halo population .