Chain cases are available but are bulky, heavy and a PITA to adjust and to remove when a wheel change or derailleur adjustment is needed. There are also nickel-plated chains which resist rusting. Just keep your chain lubed and fairly clean, which has benefits beyond rust mitigation, and don't sweat some superficial rust.
Stainless steels tend to be softer, wear faster and are more prone to galling than run-of-the-mill carbon steel and command a premium price to boot.