Hubble Space Telescope observations of the companion to the eclipsing millisecond pulsar PSR J2051-0827 have revealed its "dark" side. The R magnitude at minimum is ~26, while the difference between the side heated by the impinging pulsar radiation and the unirradiated side is ~3.3 mag. For the first time, these data show that there is an asymmetry in the optical light curve of the companion. Furthermore, significant variability is seen in the companion brightness measured after optical maximum on successive orbits. The data are modeled by a gravitationally distorted low-mass secondary star that is irradiated by the pulsar wind. These model fits indicate that the system is only mildly inclined (i ~ 40°) and the unilluminated side of the companion has a temperature likely less than 3000 K