Something is unchained when it's free from restraints that confine it. Better not leave your unchained bike outside of the library — someone might steal it!
Most people think it's fine to leave your dog unchained in the back yard for a while but consider it cruel when a dog is chained outdoors all day. To be chained is to be secured by a chain, and when you add the prefix un-, "not," you get the opposite. An unchained tiger cub can happily run back to its mother, and an unchained gate can freely swing open.