According to textbooks, no physical observable can be discerned allowing to distinguish a liquid from a gas beyond the critical point. Here we report 1 2 Ranieri et al. quasi-elastic neutron scattering measurements of the molecular self diffusion in supercritical fluid methane as a function of pressure along the 200 K isotherm (corresponding to 1.05 times the critical temperature) where we observe a clear crossover in the dynamic structure factor from a gaslike Gaussian to a liquid-like Lorentzian signal. The crossover is progressive and takes place upon compression at about the Widom line intercept. Concurrently, a sharp change in the pressure dependence of the molecular self-diffusion coefficient takes place. At considerably higher pressures, we find that the same liquid-like jump diffusion mechanism can fit the experimental data on both sides of the Frenkel line, marking the change from a non-rigid to a rigid fluid. The observation of a gas-like to liquidlike dynamical crossover in supercritical methane could have planet-wide implications, and possible industrial applications in green chemistry.