Mud is fun for you, not for your chain. Use Pedro's SynLube.
Wet, muddy trail conditions are where Pedro's SynLube Chain Lube really shines. This tough, tenacious chain lube sticks like glue to your clean chain, protecting it from both mud and driving rain, as well as the particles that creep into non-synthetic lubes. Added corrosion inhibitors keep rust away, at least until you have time to hose down your ride.