  We study hard-core bosons on the honeycomb lattice in the presence of
anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte
Carlo (QMC) technique, we extract the phase diagram of the model in terms of
the filling and the anisotropy. At half-filling we find a dimer insulator phase
near maximum anisotropy that is characterized by a finite topological
entanglement entropy $\ln(2)/2$, indicative of a fractional quantum Hall state
for bosons. We identify the presence of edge states and derive a QMC-based
method to extract and verify their chirality. Remarkably, this phase arises in
the absence of magnetic flux and without explicit lattice frustration.
