We report the detection of a radial velocity companion to the extremely low-mass white dwarf (WD) LP400-22. The radial velocity of the WD shows variations with a semiamplitude of 119 km s-1 and a 0.98776 day period, which implies a companion mass of M >= 0.37 M sun. The optical photometry rules out a main-sequence companion. Thus the invisible companion is another WD or a neutron star. Using proper-motion measurements and the radial velocity of the binary system, we find that it has an unusual Galactic orbit. LP400-22 is moving away from the Galactic center with a velocity of 396 ± 43 km s-1, which is very difficult to explain by supernova runaway ejection mechanisms. Dynamical interactions with a massive black hole like that in the Galactic center can in principle explain its peculiar velocity, if the progenitor was a triple star system comprised of a close binary and a distant tertiary companion. Until better proper motions become available, we consider LP400-22 to be most likely a halo star with a very unusual orbit.