Carry a plastic bag full of paper towels in your bike bag!
In the past year or so I've given paper towels out to 4 or 5 people who I spotted by the side of the road with grease on their fingers and a panicked or despondent look on their face. Even if they had already managed to get their chain back on, they still had to deal with thick black grease on their hands.
I've rarely seen such profuse gratitude as when I handed these people the paper towels.