Cross-magnetic-field heat transport in a quiescent pure ion plasma is found to be diffusive and to be dominated by long-range ''guiding center'' collisions. In these long-range collisions, which occur in plasmas with {lambda}{sub D} > r{sub c}, particles with impact parameters r{sub c} < {rho} {le} {lambda}{sub D} exchange parallel kinetic energy only. The resulting thermal diffusivity {chi}L is independent of plasma density n and magnetic field B. We measure a thermal diffusivity {chi} which agrees within a factor of 2 with the long-range prediction {chi}L = 0.49 n{bar v}b{sup 2}{lambda}{sub D}{sup 2} over a range of 10{sup 3} in temperature, 50 in density, and 4 in magnetic field. This thermal diffusivity is observed to be up to 100 times larger than the classical diffusivity. These long-range collisions are typically dominant in unneutralized plasmas, and may also contribute to electron heat transport in neutral plasmas.