The 1:1 complex of 1,2-ethanediol with dimethyl sulfoxide was studied using density functional theory. A network of three hydrogen bonds holds the complex together, including two in which each methyl group donates to the same hydroxyl oxygen. Four lines of evidence support the existence of methyl-donated hydrogen bonds. The interaction energy is 36 +/- 5 kJ/mol using Becke's three parameter hybrid theory with the 1991 nonlocal correlation functional of Perdew and Wang, and a moderately large basis set (B3PW91/6-311++G**//B3PW91/6-31+G**). To determine the energy of each hydrogen bond, a relaxed potential energy scan was performed in a smaller basis set to break the weaker hydrogen bonds by forced systematic rotation of the methyl groups. Two cross-checking analyses show cooperative effects that cause individual hydrogen bond energies in the network to be nonadditive. When one methyl hydrogen bond is broken, the remaining interactions stabilize the complex by storing an additional 2-3 kJ/mol. With all hydrogen bonds intact, the O[bond]H...O[bond]S hydrogen bond contributes 26 +/- 2 kJ/mol stability, and each weak methyl bond stores 5 +/- 2 kJ/mol.