I don't. The consequences of it failing are too bad for me to risk. If the chain shows any sign of going bad, I replace it. So the odds of it going bad during a trip is small. The list of things that are more likely to go wrong before a chain failure is pretty long. So I carry a tire repair kit and pump, a jump start battery, and the tools I need to remove the wheels, lube the chain, and adjust the chain. (Though I've done several 3,000 mile trips without adjusting it.)
I do carry a spare clutch cable. My bike has 40,000 miles on it. And I should just replace it instead.