My daughter speaks fluent English and learns Chinese in school. But we don't speak Chinese. n this case, is it essential that she takes extra classes in Chinese?

One way to do it "free of charge" is by joining Chinese playgroups. Try to get to know Chinese speaking moms and arrange play dates. When I'm at the playground and meet mommies who speak mandarin, I strike up a conversation. And encourage my kids to converse with theirs. This way it is less contrived