I consider my chain tool an essential in my bag - I have a Park Tools one and it's really not that big or heavy.
I had an off last year when my derailleur hanger snapped, everything locked up and the chain broke. With a chain tool, you can put the chain back together as a single speed setup to get home.
The previous time I had a chain break it was after an off - I can't remember the actual details of the mishap, but the chain got caught on something and broke as I went down.
I probably carry more tools with me than most people, but in my decades of cycling I've had all sorts of failures and have only ever once* not been able to at least patch things up enough to get home - that one time, my rear axle snapped and I had a 10-mile walk home.
(*I know, I'm tempting fate)