  The isospin-breaking correlator of the product of flavor octet vector
currents, $V^3_\mu$ and $V^8_\nu$, $\Pi^{38}_{\mu\nu}(q^2)$ is computed to
next-to-next- to-leading (two-loop) order in Chiral Perturbation Theory. Large
corrections to both the magnitude and $q^2$-dependence of the one-loop result
are found, and the reasons for the slow convergence of the chiral series for
the correlator given. The two-loop expression involves a single ${\cal O}(q^6)$
counterterm, present also in the two-loop expressions for
$\Pi^{33}_{\mu\nu}(q^2)$ and $\Pi^{88}_{\mu\nu}(q^2)$, which counterterm
contributes a constant to the scalar correlator $\Pi^{38}(q^2)$. The
feasibility of extracting the value of this counterterm from other sources is
discussed. Analysis of the slope of the correlator with respect to $q^2$ using
QCD sum rules is shown to suggest that, even to two-loop order, the chiral
series for the correlator may not yet be well-converged.
