It pains me to call someone the Greatest Living Hitter who only batted .305 on their career though (Brett, Aaron).

I may have to go with Gwynn. His first year in the majors he only played in 54 games and hit .289. Over the next 19 years he never hit below .309, won 8 batting titles, had 7 seasons hitting over .350 (including 4 in a row at ages 34-37), and he only struck out 430 times in 20 years. Lifetime avg is .338.