The most common time to drop a chain is when overtaking someone only marginally slower. Things feel awesome, for a moment. The feeling Wile E. Coyote gets when he runs off a cliff.
You look down. You realise your feet are spinning not because you're suddenly Cadel Evans below the hip following the world's swiftest leg transplant, but because you are no longer connected. The rider you just overtook will not acknowledge you standing there as they pass.
BONUS TIP: Grasp that chain like it is a king cobra, fix it, then boldly wipe your hands on your linens.
And the rest of your day. Can just go to hell.