Are there brands that sell weather-resistant chains?
Lube your chain frequently. As in every time it rains if you need to.

Depending on the drive-train, you can get Shimano or SRAM chains at places like Nashbar or Performance Bike, but even top-of-the-line, expensive chains will get rusty if they're out in the rain all the time. The same will hold with a Brooks saddle. No matter how awesome it is, if it's exposed to poor conditions without proper maintenance, it will deteriorate quickly. So lube your chain frequently, and dry it off whenever you get a chance before storing it.

Disclaimer: If you go riding around with tons of lube on your chain in dry, dusty conditions, you'll pick up lots of dirt in your drivetrain.