The first NFL running back to get 1,000 yards in a single season was a player named Beattie Feathers, of the 1934 Chicago Bears. He ran for 1,004 yards in that season.
Beattie Feathers was the first to rush for 1000 yards during a season. It was accomplished in the mid 1930's while he was playing for the Chicago Bears and was selected to the first all-NFL team for that year.