Can I repair a bicycle chain?

My neighbor's kid has a bike, a kids bike, the kind when you push the pedals backwards the bike stops. The chain on her bike keeps jumping off the teeth of the pedal and tire gear.

Upon close examination of the chain, there is a link which appears to be bent out of shape. Is there a way to repair this, or does the chain need to be replaced?

I am mechanically inclined, but not experienced. I like these kids, and would like to see happy bike riding again. Thanks for any help!
Additional: We've already tried to tighten the chain by adjusting the rear tire - this worked for a few moments and then the chain popped off again.
 
If you have enough space to move the back wheel, can you just remove the bent link from the chain and make it one shorter? If not, for a coaster brake bike, it is probably safer to replace it. Walmart sells chains for ~$10. They have to be made the same length as the current chain, but are very easy to install.
 
It would be best to replace the chain. Walmart sells standard 1/8 inch single speed chains for cheap. The chain will need to be cut to the correct size.
 
I would try to bend the link back into shape, otherwise you can buy a special link that will replace the broken one but they cost almost as much as a new chain for a kids bike would.
 
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