The first phase equilibrium data are reported for mixtures of heavier liquid hydrocarbons + methane forming structure H hydrates. Four-phase equilibrium conditions (water, liquid hydrocarbon, vapor, and structure H hydrate) were measured for three systems: methane + 2,2-dimethylbutane, methane + 2-methylbutane, and methane + methylcyclohexane. These hydrocarbons constitute a small fraction of crude oil reservoirs where they coexist with various gases, including methane. Consequently this work suggests the possibility of the natural occurrence of structure H hydrates in such natural and artificial environments, and these initial phase equilibrium data have the potential to impact industrial perspectives about hydrates.