  The recent progress towards production of near-ground state
quantum-degenerate molecules raises the issue of how such "small" molecules
behave in an optical lattice. In this Letter we show that the coupling of the
molecular orientation to the local electric field direction will provide
severalnew phenomena. In the case where the lasers forming different
crystallographic directions of the lattice are incoherent, the orientation of
the molecules is conserved (for L = 1) and a novel form of anisotropic
superfluidity can be expected. When the lasers are coherent, and the optical
lattice is such that the splitting of the rotational levels is large compared
to the centre of mass energies,an adiabaic description of the molecular
orientation is appropriate. This leads to geometric vector potentials,
pseudo-magnetic monopoles and a frustrated band structure with degenerate
minima.
