The Challenger mechanism for the methylation of arsenic is a repeating sequence of a two-electron reduction of pentavalent arsenic As(V) species to trivalent arsenic As(III) species followed by a methylation-oxidation reaction forming the successive methyl As(V) species. This unusual oxidation-reduction sequence prompted an examination of the thermodynamics of these reactions. Quantum chemical methods are employed to estimate the thermodynamic parameters for the methyl arsenic species. The sequence is thermodynamically favored at neutral pH for redox potentials with pe < 0 and methyl cation activities pCH3+ < -3 to -7 depending on the precise situation analyzed. The observed distribution of methyl arsenic species in human urine, which is remarkably constant across many studied populations, can be reproduced using an equilibrium model if the formation of TMA species is prevented. The estimated thermodynamic parameters are sufficiently accurate to evaluate questions of thermodynamic plausibility but not the precise details of speciation.