  We calculate the mean-field phase diagram of a zero-temperature, binary Bose
mixture on a square optical lattice, where one species possesses a
non-negligible dipole moment. Remarkably, this system exhibits supersolidity
for anomalously weak dipolar interaction strengths, which are readily
accessible with current experimental capabilities. The supersolid phases are
robust, in that they occupy large regions in the parameter space. Further, we
identify a first-order quantum phase transition between supersolid and
superfluid phases. Our results demonstrate the rich features of the dipolar
Bose mixture, and suggest that this system is well-suited for exploring
supersolidity in the experimental setting.
