Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble were used to obtain vapor-liquid coexistence curves for a series of alkanes physisorbed on a flat gold substrate. The critical temperatures and densities of n-alkanes from methane to decane as well as the branched molecules 2-methylpropane, 2,2-dimethylbutane, and 2,3-dimethylbutane were determined through a mixed-field analysis. The ratio of the 2D (two-dimensional) to the 3D (three-dimensional) critical temperature was found to depend weakly on the chain length for n-alkanes, decreasing from T-c(2D)/T-c(3D) = 0.38 for methane to T-c(2D)/Tr-c(3D) = 0.31 for n-decane. In contrast to typical bulk fluid behavior, the branched isomers were found to have higher critical temperatures than their linear counterparts.