You don't need to carry a chain tool. Just carry one of those quick links. If a chain breaks, it will be because the pin separated from an outside link. If one pin pulls out, the whole outer plate will have to pull itself off before the chain separates. Thus, you are only missing one outer link. The quick link requires no tools to install. You DO NOT want to be messing with a chain tool attached to a multi-tool when dealing with modern 10-speed chains; the tolerances for the pin are too close. If you use a chain tool to make a field repair, you won't be able to get the pin in the right place. The chain will break again at the point you riveted it.

On my fixie, I just carry a 1/8" master link. I use my keys or tiny pocket knife on my key ring to slide in the circlip.

Luis