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 nonzero momenta, defying the paradigm. This becomes possible when the atoms are confined in the -orbital Bloch band of an optical lattice rather than the usual -orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or -density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the -orbital band and propose an “energy blocking” mechanism by Feshbach resonance to protect them from decaying to the lowest -orbital band. 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.