Breaking a chain on the road

[KevinK]

From a different thread, Weisan said:

"I get into a time-trial position and pull my buddy during the last few miles trying to make up time lost b'cos my chain broke earlier on a nasty climb and my pal had to stop for about 10 mins waiting for me to fix it."

How do you fix a chain on the road? I've never broken a chain, and never even considered carying a chain tool. So after 25+ years of riding/racing, all of a sudden you got me nervous about breaking a chain! How and where does it break? Is it at the quick-link? Did the chain show obvious signs of wear before it broke? As my wife says, I come from a long line of worriers. Please help ease my troubled mind!

Kevin
Eugene, OR