In recent years, the long-standing belief that beyond the critical point, matter exhibits no clear transition between liquid-like and gas-like states has been questioned. A line on the phase diagram, the Frenkel line, has been proposed which does separate matter into liquid-like and gas-like states beyond the critical point. However, a direct experimental proof of the existence of the Frenkel line has proved elusive.If the Frenkel line does exist, the consequences are wide-ranging; from our understanding of thermodynamics, to use of supercritical fluids in the food, chemical and power industries, to our understanding of the interiors of gas-giant planets.We propose neutron diffraction experiments on fluid methane to elucidate whether or not the Frenkel line exists, building on the tentative evidence provided by our Raman spectroscopy and X-ray diffraction experiments.