The light rare earth phosphate mineral monazite contains high concentrations of Th and U and thus should have potential as a (U-Th)/He thermochronometer. New 4He diffusion experiments confirm this potential but suggest that the bulk closure temperature may be so strongly compositionally dependent that successful applications will require careful sample characterization prior to (U-Th)/He dating. Three experiments were performed on single crystals of Monazite 554, a material that has been used as a standard for Th-Pb ion microprobe geochronology. The data from each experiment yielded a linear array on an Arrhenius diagram, consistent with simple diffusion behavior. However, the diffusion parameters indicated for each grain were statistically different, indicating closure temperatures (assuming a cooling rate of 10¿C/Myr) of 206 ¿ 24¿C, 230 ¿ 4¿C, and 286 ¿ 13¿C. X-ray compositional maps of Monazite 554 illustrate a possible cause of this discrepancy: strong and geometrically complex chemical zoning that varies from grain to grain and likely corresponds to several episodes of growth and dissolution. If He diffusivity in monazite is compositionally controlled, individual crystals with such inconsistent zoning (which is typical of naturally occurring monazites) should have different bulk closure temperatures.