You will find it a lot nicer to work on when it's clean too.

I'll tell you what I do, and don't laugh, because it works pretty well.
I run my chassis through the dishwasher. I usually spray the top side of the chassis with some spray nine or Super Clean and let it sit for a minute or so before tossing it in the dishwasher. You will want to take off the cardboard protector on the back of the neckboard, but other than that, put it in the way it is. Set the dishwasher to a nornal wash cycle, turn off the dry cycle *VERY IMPORTANT*. Oh, and don't put in any soap either. Once the dishwasher is done, you can either let the chassis air dry for a few days, or use compressed air to blow the worst of the water off the chassis and use the oven to dry it out. To use the oven, heat it up to 200deg F, turn it off and put the chassis in on a cookie sheet. Usually by the time the oven cools off, the chassis should be dry. You may have to repeat this process twice to get it totally dry if you can't blow the worst of the water off with air.
Don't expect to get the chassis totally spotless though, some stuff will be so baked on it will likely never come totally clean.