  We investigate the unconventional Bose-Einstein condensations (BEC) with the
orbital degree of freedom in the 3D cubic optical lattice, which give rise to
various exotic features absent in conventional scalar and spinor BECs. Orbital
angular momentum moments are formed on lattice sites breaking time-reversal
symmetry spontaneously. Furthermore, they exhibit orbital frustrations and
develop a chiral ordering selected by the "order-from-disorder" mechanism.
