The use of trimethylgallium (TMGa) as the gallium source during epitaxial growth of GaAs often leads to high levels of carbon incorporation. Using temperature programmed desorption, high-resolution electron energy loss spectroscopy (HREELS), and static secondary ion mass spectroscopy (SSIMS), we have identified a likely carbon incorporation pathway initiated by methyl group dehydrogenation. Methyl group dehydrogenation is evidenced by a small amount of hydrogen evolution around 430-degrees-C. Extended TMGa exposures in this temperature regime yield substantial coverages of methylene (CH2) adsorbate that is detected by HREELS and SSIMS. The CH2 adsorbate undergoes further reaction at higher temperature, yielding acetylene (C2H2), H-2, and CH3 radicals as desorption products at approximately 550-degrees-C. All of these products can be attributed to a mechanism involving CH2 dehydrogenation, hydrogenation, and recombination reactions. The rate of CH3 dehydrogenation is consistent with carbon doping levels typically obtained by metalorganic molecular beam epitaxy (MOMBE) and related techniques. High temperature exposure to arsine (AsH3) consumes the CH2 adsorbate, apparently by hydrogenating them back to CH3 groups that then desorb. This observation explains why carbon doping is lower during atomic layer epitaxy as compared to MOMBE.