We present the discovery and spectroscopic identification of two very high proper-motion ancient white dwarf stars, found in a systematic proper-motion survey. Their kinematics and apparent magnitude clearly indicate that they are halo members, while their optical spectra are almost identical to the recently identified cool halo white dwarf WD 0346+246. Canonical stellar halo models predict a white dwarf volume density that is 2 orders of magnitude less than the rho approximately 7x10-4 M middle dot in circle pc-3 inferred from this survey. With the caveat that the sample size is very small, it appears that a significant fraction, approximately 10%, of the local dark matter halo is in the form of very old, cool, white dwarfs.