That white rust, aka zinc oxide, is a sign that the zinc in the galvanized coating is doing its job. Somewhere else on the chain, or on some ferrous metal in conduction with the chain, is an exposed surface where iron would be rusting EXCEPT that the zinc on the chain, being more active electrolysiswise, is "rusting," aka oxidizing, instead. That's why it is refered to as a sacrificial coating. And when it is gone, baby, the chain itself is next!
Yup, same zinc oxide found in ointments used to protect skin from sunburn.