  We predict the robust existence of a novel quantum orbital stripe order in
the $p$-band Bose-Hubbard model of two-dimensional triangular optical lattices
with cold bosonic atoms. An orbital angular momentum moment is formed on each
site exhibiting a stripe order both in the superfluid and Mott-insulating
phases. The stripe order spontaneously breaks time-reversal, lattice
translation and rotation symmetries. In addition, it induces staggered
plaquette bond currents in the superfluid phase. Possible signatures of this
stripe order in the time of flight experiment are discussed.
