  We consider a counting problem in the setting of hyperbolic dynamics. Let
$\phi_t : \Lambda \to \Lambda$ be a weak mixing hyperbolic flow. We count the
proportion of prime periodic orbits of $\phi_t$, with length less than $T$,
that satisfy an averaging condition related to a H\"older continuous function
$f: \Lambda \to \mathbb{R}$. We show, assuming an approximability condition on
$\phi$, that as $T \to \infty$, we obtain a central limit theorem.
