No, do not need a chuck to turn any things you can make on a lathe. On every woodturning message board questions about lathes, turning tools, and chuck major topics. No doubt a chuck does make life easier, but will not really make you a better woodturner.
Like the article says you can pay a little or a lot for a woodturning chuck and walk you through chuck basics. I disagree with what articles said about faceplates, screws, and glued waste blocks due to design of a piece and safety. People often use clue blocks mounted in their chucks today too!
If understand the basicS this article provides selecting and buying a woodturning chuck you can afford lot easier.