The initial reaction of the As-rich c(2×8) GaAs(100) surface with trimethylgallium (TMGa) has been studied by x-ray and ultraviolet photoemission. TMGa was found to chemisorb dissociatively at temperatures below 300°C with many of the methyl radicals remaining on the surface. Bonding requirements and steric effects limit the saturation coverage to about 0.1 monolayer. At temperatures above 300°C, TMGa was observed to dissociate on the surface, release all the methyl groups, and deposit Ga up to a self-limiting coverage. This process is most effective at high temperatures. We propose a model for the temperature dependence of the chemisorption which explains and unites many reported observations in the atomic layer epitaxy of GaAs using TMGa and arsine.