  We study the conformal properties of pseudo-scalar (parity-odd) operators in
four-dimensional field theory. Such operators include the topological term in a
gauge theory and the Yukawa coupling. We show that a single operator of this
type cannot be a conformal primary on its own. This is only possible for
certain mixtures of pseudo-scalar operators like the chiral Lagrangian of
${\cal N}=4$ super-Yang-Mills theory. We examine the detailed mechanism of
conformal symmetry breakdown and derive an anomalous conformal Ward identity.
We explore a possible link between this conformal anomaly and the axial
anomaly.
