  We study the topological properties of elementary excitations in a staggered
$p_x \pm i p_y$ Bose-Einstein condensate realized in recent orbital optical
lattice experiments. The condensate wave function may be viewed as a
configuration space variant of the famous $p_x+ ip_y$ momentum space order
parameter of strontium ruthenate superconductors. We show that its elementary
excitation spectrum possesses Dirac bosons with $\pi$ Berry flux. Remarkably,
if we induce a population imbalance between the $p_x+ip_y$ and $p_x-ip_y$
condensate components, a gap opens up in the excitation spectrum resulting in a
nonzero Chern invariant and topologically protected edge excitation modes. We
give a detailed description on how our proposal can be implemented with
standard experimental technology.
