Global U(1) R-symmetry and conformal invariance of (0,2) models

We derive a condition under which (0,2) linear sigma models possess a "left-moving" conformal stress tensor in Q₊ cohomology (i.e. which leaves invariant the "right-moving" ground states) even away from their critical points. At the classical level this enforces quasihomogeneity of the superpotential terms. The persistence of this structure at the quantum level on the worldsheet is obstructed by an anomaly unless the charges and superpotential degrees satisfy a condition which is equivalent to the condition for the cancellation of the anomaly in a particular "right-moving" U(1) R-symmetry.