We report the discovery of a new dwarf galaxy, Andromeda XXIX, using data from the recently-released Sloan Digital Sky Survey DR8, and confirmed by Gemini North telescope Multi-Object Spectrograph imaging data. And XXIX appears to be a dwarf spheroidal galaxy, separated on the sky by a little more than 15 degrees from M31, with a distance inferred from the tip of the red giant branch of 730kpc+/-75kpc, corresponding to a three dimensional separation from M31 of between 205kpc and 227kpc (close to M31's virial radius). Its absolute magnitude, as determined by comparison to the red giant branch luminosity function of the Draco dwarf spheroidal, is M_V = -8.3+/-0.4. And XXIX's stellar populations appear very similar to Draco's; consequently, we estimate a metallicity for And XXIX of [Fe/H]\sim-1.8. The half-light radius of And XXIX is 360pc+/-60pc and its ellipticity is 0.35+/-0.06, typical of dwarf satellites of the Milky Way and M31 at this absolute magnitude range.