  We study the trace anomaly of a Weyl fermion in an abelian gauge background.
Although the presence of the chiral anomaly implies a breakdown of gauge
invariance, we find that the trace anomaly can be cast in a gauge invariant
form. In particular, we find that it does not contain any odd-parity
contribution proportional to the Chern-Pontryagin density. The latter would be
allowed by the consistency conditions. We perform our calculations using
Pauli-Villars regularization and heat kernel methods. The issue is analogous to
the one recently discussed in the literature about a conjectured contribution
of an odd-parity term to the trace anomaly of a Weyl fermion in curved
backgrounds.
