Answer: Otis Nixon
Otis Nixon began his MLB career in 1983 at the age of 24 with the New York Yankees. He was born in North Carolina which is considered Braves country. He came to play for his nearest team in 1991.
Nixon had a solid career and is underappreciated because of the fact he has no all-star appearances or individual awards. However, he played consistently for 17 seasons and that should account for something.