The ancient Greeks chewed a gum made of the resin from the mastic tree. In fact the reason it’s called the mastic tree in the first place is from the Greek word to chew; “mastichan”. Not to be outdone, the Romans also liked chewing gum after a hard day’s conquering and pillaging.
Meanwhile the ancient Mayan civilisations were chewing a gum made from chicle. This is the same stuff Peppersmith gum is made from and you can read more about it here.