Or you might be on a training ride 40 miles from home with no cell signal.
Why would a chain break? Well, the outer plates are connected together with pins that are press fit into the plates. There is a tolerance on the manufacture of these pins and plates and maybe you have a combination of a plate where the hole is slightly too large and the pin is slightly too small. Under stress it pops. Or maybe when the shop took it apart during your tuneup, the new kid put the chain back on. No matter. You're standing beside the road with a bicycle and your chain is 20 feet behind you, laying in the road. Let's get that puppy back together and back in the race.
Note: There might be a sag wagon. Maybe a half hour away. Maybe somebody knows how to fix your chain. Maybe.
Let review the tools you need to fix the chain. It's called a chain breaker tool. Odd name, since your chain is already broken. Many multi-tools, such as the Crank Brothers 19 pictured below come with one built in.
The chain tool is the threaded piece with the pin sticking out.
That's all you need. Except for a repair link. Maybe like the KMC Missing Link shown here.
These are fairly cheap. Note that they come in 9-speed, 10-speed, or 11-speed. The 9-speed are $7 for 6 pair, the 10 speed are $12 for 6 pair, and the 11 speed are $28 for 6 pair. Who the hell needs an 11 speed on a time trial bike anyway? But I digress.
Now that you've got the parts, let's put the chain back on. First thing we have to do is remove the broken link. Note that on you chain you have outer plates and inner links. We want the two ends that we're going to connect to both be inner links. That means we're going to need to remove the outer plates from one end of the broken chain.
Note that the left end has the inner link. Let's leave that alone. See the broken outer plates on the right. Let's remove these. So get out the chain break tool and let's break a chain. Your hand will get very dirty. Wipe them on the black part of your shorts.
Line up the pin on the chain break tool with the pin on the loose end of the chain. Gradually tighten the tool until you feel the pin on the tool pressing the pin on the chain very solidly. Now use some muscle and crank down. We want to push this pin all of the way out.
Now you can see that you have two chain ends, both with the inner links exposed. The next step is to thread the chain back on the bike. Before you do, shift both the front and rear derailleurs to the smallest (number of teeth) cogs. This will make putting the chain on a bit easier.
In the rear, the chain will go over the cog, around the guide pulley, and around the idler pulley in a zig-zag fashion (or an S-shape). Be careful threading the chain through, because most derailleurs will have a retaining tab on the cage. You want the chain to go between the cage and the pulley. Note the two tabs on this derailleur.
Put the other end of the chain through the front derailleur. Here, I deliberately do not put the chain on the front sprocket and just wrap it around the bottom bracket. This will make the ends of the chain easier to connect.
Now let's join the chain together. Take the repair link that you have stuffed in your tool kit and assemble it to the bike.
Now the chain is together. Take a quick look and make sure that both sides are connected.
Put you chain back on the front chainring. Spin the pedals around and make sure everything seems to work.
Depending on the type of connector you use, it might need to snap in place. If so, rotate the chain around until the connector is on top. With the rear wheel on the ground, put some downward pressure on a pedal and the chain will snap into final position.
See in the picture above that the pin is in the smaller section of the hole on the repair place.
Although this sounds complicated, this repair can be made in 5 minutes. I would suggest that everyone practice removing pins from an old chain as this is probably the hardest part. Also, verify that the chain is through the rear derailleur correctly before installing the repair link.