  The breaking of time reversal symmetry via the spontaneous formation of
chiral order is ubiquitous in nature. Here, we present an unambiguous
demonstration of this phenomenon for atoms Bose-Einstein condensed in the
second Bloch band of an optical lattice. As a key tool we use a matter wave
interference technique, which lets us directly observe the phase properties of
the superfluid order parameter and allows us to reconstruct the spatial
geometry of certain low energy excitations, associated with the formation of
domains of different chirality. Our work marks a new era of optical lattices
where orbital degrees of freedom play an essential role for the formation of
exotic quantum matter, similarly as in electronic systems.
