  We derive a condition under which (0,2) linear sigma models possess a
``left-moving'' conformal stress tensor in $\bq$ 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.
