  The large mass of the $\eta'$ meson indicates that a sizeable gluon component
is present in the meson wave function. However, the $\chi_{c0}$ and $\chi_{c2}$
decays to $\eta'$ mesons, which proceed via a purely gluonic intermediate state
and we would therefore na\"{i}vely expect to be enhanced by such a component,
are in fact relatively suppressed. We argue that this apparent contradiction
may be resolved by a proper treatment of interference effects in the decay. In
particular, by accounting for the destructive interference between the quark
and gluon components of the $\eta'$ distribution function, in combination with
a model for strange quark mass effects, we demonstrate that the observed
$\chi_{c(0,2)}\to\eta(')\eta(')$ branching ratios can be reproduced for a
reasonable gluon component of the $\eta'$, $\eta$ mesons.
