We employ a double capsule technique to determine the solubility of CH4 in haplobasaltic (Fe-free) liquid under conditions of constrained methane fugacity, fCH4, at pressures of 0.7-3GPa at 1400-1450°C. Dissolved C-O-H species are examined with FTIR and Raman spectroscopy, and CH4 and CH3- are the only C-bearing species detected. Carbon solubilities are quantified using SIMS, range from 70 to 480ppm when calculated as CH4, and increase with pressure. Concentrations are parameterized with a thermodynamic model and are found to be related to fCH4 and pressure. Application of this thermodynamic model shows dissolved CH4 contents of graphite-saturated magmas are little-influenced by pressure for conditions of fixed fO2 relative to metal-oxide buffers and fixed total H content. Because fCH4 of graphite-saturated systems increases with the square of hydrogen fugacity, dissolved fCH4 increases with decreasing fO2 and increases exponentially with increasing total H content. The experimentally-observed increase with pressure is related to variations in fO2 and H content. Dissolved CH4 contents of Martian magmas in their source regions are small, such that it is unlikely that magmatic CH4 is a principal contributor to greenhouse conditions early in Martian history. Concentrations of dissolved C-O-H volatiles in a magma ocean early in the history of a terrestrial planet may be diminished by reducing conditions, leading to development of a massive atmosphere and a greatly decreased inventory of volatiles stored in planetary interiors at the outset of planetary history. Dissolution of methane may enhance the retention of C in the silicate Earth during core formation, but experimental evaluation of its influence on metal/silicate partitioning of C requires careful matching of the magmatic H concentration between experiments and natural systems.