Based on CO (2-1) observations obtained with the Swedish-ESO Submillimeter Telescope, the distribution of molecular material associated with the Wolf-Rayet ring nebula NGC 2359 has been determined. The angular resolution is 22", and the velocity resolution is 0.33 km s-1. Three molecular components are detected in the direction of the nebula. The bulk of the molecular gas is observed at 54 km s-1 and follows the southeastern border of the nebula.