The attenuation of hexapole-focused CH3Cl molecular beams has been studied as a function of inert gas and nitrogen gas pressure in a hexapole-collision cell, Cross sections have been determined as a function of relative velocity, using seeded beams, and as a function of specific \JKM] states through variation of the electric field strength in the hexapole. Beam attenuation is attributed to rotationally inelastic collisions in which a beam molecule following a focusing upper Stark state (KM < 0) trajectory through the hexapole field is converted by a Delta M or Delta J, Delta M transition into a nonfocusing rotational state (KM = 0 or KM > 0), which then follows a modified, nonfocusing trajectory and is lost from the beam. Experimental cross sections are in the range from 200 to 670 Angstrom(2), consistent with collisions controlled by a long-range interaction (8 to 15 Angstrom) involving the transfer of a few J mol(-1) of energy. Collision cross sections estimated using a van der Waals interaction potential with dispersion and dipole-induced dipole terms suggest that cross sections of these magnitudes most probably correspond to collisions in which only the M quantum number changes.