Greasy hands are no fun and as documented in previous posts, I tie an old sock to my frame or rack in case I have on road repairs. I just put the sock over my hand and do what I need to do, and then toss the sock and replace it with another.
Reader Spannerrash was having problems with chain slips and came up with a hack to keep his hands from getting greasy. The solution is effective, but those with chain slip issues might also benefit from visits to two great web sites that address this issue, as well as just about any bike related repair issue you can think of: Sheldon Brown and The Bicycle Tutor.
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I had a series of chain slips that jammed the chain in the rear forks.
I became fed up with greasy hands (that I couldn't clean on the side of the road) so I made a small hook to grab the chain and allows me to put the the chain back in place grease free. Purists will scream and groan that I allowed this to happen but, hey, that's life. The hook out of a piece of 3mm - 1/8th approx wire I found (I think its brass).