I think Chita just sang exceptionally well from early in her career. She clearly had an excellent instrument. Whether her excellent use of it was instinctive or trained (or a combination of both), I think she already sounds great on the cast recordings of West Side Story and both Bye Bye Birdie cast recordings she is on (Broadway and London). She was such a great dancer that people focused on that, but her talents and skills were such that she might well have had a major career in musicals even if she hadn't been such a great dancer.
