  We show that Bose-Einstein condensates in optical lattices with broken
time-reversal symmetry can support chiral edge modes originating from
nontrivial bulk excitation band topology. To be specific, we analyze a
Bose-Hubbard extension of the Haldane model, which can be realized with
recently developed techniques of manipulating honeycomb optical lattices. The
topological properties of Bloch bands known for the noninteracting case are
smoothly carried over to Bogoliubov excitation bands for the interacting case.
We show that the parameter ranges that display topological bands enlarge with
increasing the Hubbard interaction or the particle density. In the presence of
sharp boundaries, chiral edge modes appear in the gap between topological
excitation bands. We demonstrate that by coherently transferring a portion of a
condensate into an edge mode, a density wave is formed along the edge owing to
an interference with the background condensate. This offers a unique method of
detecting an edge mode through a macroscopic quantum phenomenon.
