I weigh 200lbs and live in Colorado where we DO
have stand and grunt climbs.
I have never, ever broken a chain.
I run a PC870 on my old hardtail which is a work commuter now. This bike carries me and my 15lbs or so laptop bag, and I nail it pretty hard when in automobile traffic, especially when I forget to shift out of a tall gear at an intersection.
My mountain bike has a Shimano XTR CN7701. I have ridden with that chain all over the Front Range and in Moab. If any of you have ridden Slickrock, I rode up "The Wall" a couple of times with that setup...no chain breakage.
Chili may have hit on it: make sure you are shifting properly and efficiently. Also make sure it is clean and well lubed, with the excess wiped off.
And for the record, I am a former hockey player with decent leg strength. If anyone can break a chain, it should be me!