After removing a chain a few days ago and having it soaking in mineral spirits to clean it, I decided since it's almost worn out and the wife's out of town with the kid at a swim meet, I'd put the chain in the dishwasher and see what happened.

It's nice and shiny. And as clean as a whistle.

Only issues I can see are:

1. Dishwasher detergent may not be good for chain life
2. Getting caught