There has been interest recently concerning when a left ordered group is locally indicable. Chiswell and Kropholler proved that every left ordered solvable-by-finite group is locally indicable, while Bergman gave examples of left ordered groups which are not locally indicable. This paper proves that every left ordered elementary amenable group is locally indicable. Every solvable-by-finite group is elementary amenable, and every elementary amenable group is amenable. The author leaves it as an open problem as to whether every left ordered amenable group is locally indicable.