Pure methane-oxygen mixtures in liquid rocket engines lead to extreme pressure and temperature conditions that are prohibitive for most of the experimental setups. Hence, there is very little data on such flames in the literature, especially concerning the laminar flame speed, often limited at atmospheric pressure. The recent development of methalox rocket engines, which design process often requires CFD calculations, brings this lack of data to the forefront. Indeed, the CFD simulations require valid chemical schemes in the real operating conditions. To address this problem, flame measurements have been performed in a special isochoric combustion chamber with full optical access (OPTIPRIME) developed at ICARE. An extensive database in conditions never tested before is generated for several equivalence ratios, temperature and pressure ranges. Multiple chemical mechanisms were then compared to those results, showing various levels of agreement. Hence, the best mechanism from the literature on OPTIPRIME results and other literature experimental data was selected. A sensitivity analysis was performed to identify key chemical reactions controlling the flame speed. These key reactions could later be tuned by an optimization process to perfectly match the experimental results. Finally, additional measurements were performed in order to develop a correlation to build a future flame speed database under rocket engines relevant conditions.