  The paradigm of Bose-Einstein condensation has been associated with zero
momentum to which a macroscopic fraction of bosons condense. Here we propose a
new quantum state where bosonic alkali-metal atoms condense at non-zero
momenta, defying the paradigm. This becomes possible when the atoms are
confined in the p-orbital Bloch band of an optical lattice rather than the
usual s-orbital. The new condensate simultaneously forms an order of
transversely staggered orbital currents, reminiscent of orbital
antiferromagnetism or d-density wave in correlated electronic systems but
different in fundamental ways. We discuss several approaches of preparing atoms
to the p-orbital and propose an ``energy blocking'' mechanism by Feshbach
resonance to protect them from decaying to the lowest s-orbital. Such a model
system seems very unique and novel to atomic gases. It suggests a new concept
of quantum collective phenomena of no prior example from solid state materials.
