  We perform a calculation of the isospin and hypercharge vector current
propagators ($\Delta_{V33}^{\mu\nu}(q^2)$ and $\Delta_{V88}^{\mu\nu}(q^2)$) to
two loops in chiral perturbation theory. The analysis is carried out with
straightforward Feynman diagram methods by making appropriate use of external
vector sources. Counterterms from the ${\cal O}(q^6)$ chiral lagrangian,
required to absorb divergences and scale dependence encountered at the two-loop
level, are constructed. Our final results are finite, covariant, and
scale-independent. Several applications are described, including a comparison
of the two-loop isospin vector spectral function with data and the construction
of new chiral sum rules.
