With around 4000 miles on it, it was about time to change the chain on my commuter bike.
As you can see from the photo, the pins were quite worn. This is the cause of what is called "chain stretch."
Bike chains do get longer with use and wear, but they don't actually "stretch"; it's the accumulated wear of the pins like the one shown here that add up to the extra length. And when a chain is a little longer, it doesn't fit into the sprockets very well anymore.
Now that I have a new chain (and new "cassette" of rear gears), the bike literally runs like new. I should have done this repair a long time ago! I can't believe how smooth and quiet the bike is now.