We report on observations of the J = 2-1 line of CO to study the distribution and kinematics of the molecular gas in the bipolar planetary nebula NGC 2346. The data were obtained with the National Radio Astronomy Observatory 12-m telescope whose beamsize (FWHM = 30″) partially resolves the CO emitting region. A map of the velocity integrated emission shows a roughly rectangular distribution, approximately 53″ × 34″, oriented along the minor axis of the optical nebula. The CO spectrum towards the central star system is strongly double peaked. The mapping data show that this results from two distinct regions which are offset south-east and north-west of the center with radial velocities which are, respectively, larger and smaller than that of the star system. Overall the CO data are consistent with an expanding and partially disrupted distribution of molecular gas around the waist of the optical nebula. Mass estimates confirm that a substantial amount of the matter ejected by the star system is still in molecular form.