Surface reactions of CH2I2 on gallium-rich GaAs(100)-(4 x 1), studied by temperature programmed desorption and X-ray photoelectron spectroscopy (XPS), show CH2I2 adsorbs dissociatively at liquid nitrogen temperatures to form surface chemisorbed CH2(ads) and I(ads) species. Controlled hydrogenation of a fraction of the CH2(ads) species in the chemisorbed layer by the background hydrogen radicals results in a surface layer comprising both CH3(ads) and CH2(ads) species. This hydrogenation step initiates a plethora of further surface reactions involving these two species and I(ads). Thermal activation leads to three sequential methylene insertions (CH2(ads)) into the CH3-surface bond to form three higher alkyl (ethyl (C2), propyl (C3), and butyl (C4)) species, which undergo beta-hydride elimination to evolve the respective higher alkene (ethene, propene, and butene). In competition with beta-hydride elimination, reductive elimination of the ethyl and propyl species with I(ads) occurs to liberate the respective alkyl iodide. Beta-hydride elimination in the alkyls, in the temperature range 420-520 K, is the more dominant pathway, and it is also the rate-limiting step for further chain propagation. The evolution of the alkyl iodides represents the only pathway for the removal of surface iodines in this study and is different from previous investigations where gallium and arsenic iodide etch products (GaI(x), AsI(x) (x = 1-3)) formed instead. The desorption of methane and methyl iodide, formed from surface CH3(ads) species at high temperatures by the reaction between surface methylenes and hydrogens eliminated from the surface C2-C4 alkyls, terminates the chain propagation. We discuss the reaction mechanisms by which the observed reaction products form and postulate reasons for the reaction pathways adopted by the surface species.