  We report on the detection of the two shortest period non-interacting white
dwarf binary systems. These systems, SDSS J143633.29+501026.8 and SDSS
J105353.89+520031.0, were identified by searching for radial velocity
variations in the individual exposures that make up the published spectra from
the Sloan Digital Sky Survey. We followed up these systems with time series
spectroscopy to measure the period and mass ratios of these systems. Although
we only place a lower bound on the companion masses, we argue that they must
also be white dwarf stars. With periods of approximately 1 hour, we estimate
that the systems will merge in less than 100 Myr, but the merger product will
likely not be massive enough to result in a Type 1a supernova.
