The first detailed atmospheric analysis of the DQ white dwarf G35 - 26 is presented. The analysis is based on published spectra and on helium-rich, homogeneous, blanketed LTE models containing carbon, hydrogen, and small amounts of N, O, and Ca, and on the assumption that G35 - 26 is a single star. The observed spectra are fitted against the model spectra, and T(eff), log(g), and abundances of H, He, C are determined along with upper limits on N, O, and Ca. The mass and zero temperature Hamada-Salpeter (ZTHS) radius, distance, parallax, and tangential velocity are derived. The mass, 1.2-1.33 solar, is the highest yet observed for a single white dwarf if the star is on the ZTHS relation. O + Ne + Mg white dwarf in this mass range are predicted by theory and G35 - 26 may be the first such object discovered. Given an ZTHS radius, the distance is between 33 and 69 pc.