A novel soybean cultivar, designated 0509237, is disclosed. The invention relates to the seeds of soybean cultivar 0509237, to the plants of soybean 0509237 and to methods for producing a soybean plant produced by crossing the cultivar 0509237 with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar 0509237 with another soybean cultivar.