Recent laboratory experiments on methane hydrate formation in the presence of Na-montmorillonite, a clay mineral found coexistently with hydrates in oceanic sediments, suggest that clay surfaces may facilitate methane hydrate crystallization from aqueous solution. Monte Carlo and molecular dynamics simulations were carried out to determine whether stable methane clathrates could in principle form in the interlayers of hydrated Na-montmorillonite in equilibrium with seawater under ambient conditions. Stable interlayer methane clathrate structures were indeed found to occur under pressures as low as 10 atm and at temperatures as high as 300 K in simulations of a three-layer hydrate of Na-montmorillonite containing 0.5 CH4 per clay mineral unit cell. This result is consistent with a "thermodynamic promotion effect" of clay mineral surfaces on hydrate formation. Visualization of local methane clathrate structure in the 0.5 CH4 per unit cell system revealed that the methane molecule is nested on a hexagonal ring of clay surface oxygens while surrounded by a clathrate-like water structure. The calculated CH4-O Coordination number was 20-22, in agreement with previous simulations and with neutron diffraction data on methane hydrate formation in bulk solution. Our MD simulations indicated that the power spectrum of the interlayer hydrate was essentially the same as that for the hydrate in bulk water. Higher methane loading than 0.5 CH4 per unit cell was found to destabilize the hydrate structure similarly to a temperature increase. On the basis of these simulations, methane hydrate is proposed to occur in natural sediments with a portion of a clay mineral surface actively involved in promoting clathrate formation.