Thank you for getting back to me, Lisa. Chasing and nipping are part of the mating ritual, but they don't usually do any damage. You're right that it's the males who chase, and only males develop breeding tubercles. However, it's very possible that you have three males. The smaller one may simply not have reached breeding condition yet. When no females are present, males will chase each other. Chasing can also be a playful behavior. When it develops into actual aggression, it is because the fish are overcrowded. In a tank as big as yours, that should certainly not be a problem.
At this point, I would just keep an eye on the situation. You don't know for sure that the smaller fish damaged the fins, and there could be other ways this could have happened. If you see any aggressive biting occurring, you may have to separate this fish. Otherwise, I wouldn't do anything at this point. Goldfish do like a little company, so separation shouldn't be done unless it's necessary.
I would test the water. In a newly set-up tank, the nitrogen cycle has to be established. Excessive ammonia or nitrites in the water can cause fin damage. If you see any red streaks on the fins or body, that is another sign of this problem. Here's a website where you can read more about cycling and how to handle it:http://animal-world.com/encyclo/fresh/information/CycleAquarium.php
You may want to put in some aquarium salt (1 tablespoon per 5 gallons of water) to help with healing. Alternatively, you could use StressCoat. They can even be used safely together, if you want.
So, test your water, monitor the behavior, and add aquarium salt and/or StressCoat to the tank.
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