Look closely at that new goldfish. Do you see any tiny white pimples on his gills? We recently adopted 3 fish which had been in a 10 gallon tank all their lives and when placed in my 55 gallon tank they went nuts and started spawning. I think this is probably the chase behavior you are seeing. Best thing is to leave all the fish together and do thier spawning routine. In a day or so after the female has expelled her eggs, the chasing behavoir will stop. The fish will probably eat all the eggs and unless you remove them from the tank, you won't have to worry about babies.