  We prove the existence of topological rings in (0,2) theories containing
non-anomalous left-moving U(1) currents by which they may be twisted. While the
twisted models are not topological, their ground operators form a ring under
non-singular OPE which reduces to the (a,c) or (c,c) ring at (2,2) points and
to a classical sheaf cohomology ring at large radius, defining a quantum sheaf
cohomology away from these special loci. In the special case of Calabi-Yau
compactifications, these rings are shown to exist globally on the moduli space
if the rank of the holomorphic bundle is less than eight.
