  We investigate finite-volume effects in the hadronic vacuum polarization,
with an eye toward the corresponding systematic error in the muon anomalous
magnetic moment. While it is well known that leading-order chiral perturbation
theory does not provide a good description of the hadronic vacuum polarization,
it turns out that it gives a much better representation of finite-volume
effects. Indications are that finite-volume effects cannot be ignored when the
aim is a few percent level accuracy for the hadronic contribution to the muon
anomalous magnetic moment, even when $m_\pi L \sim 4$ and $m_\pi \sim 200$ MeV.
