We present observations of an optically-faint quasar, RD J114816.2+525339, discovered from deep multi-color observations of the field around the z = 6.42 quasar SDSS J1148+5251. The two quasars have a projected separation of 109 arcsec and both are outliers in r-z versus z-J color-color space. Keck spectroscopy reveals RD J114816.2+525339 to be a broad-absorption line quasar at z = 5.70. With z_AB = 23.0, RD J114816.2+525339 is 3.3 mag fainter than SDSS J1148+5251, making it the faintest quasar known at z>5.5. This object was identified in a survey of ~2.5 square degrees. The implied surface density of quasars at these redshifts and luminosities is broadly consistent with previous extrapolations of the faint end of the quasar luminosity function and supports the idea that active galaxies provide only a minor component of the reionizing ultraviolet flux at these redshifts.