HYPERCOORDINATE carbonium ions can be formed by protonating saturated hydrocarbons with superacids(1-3). As this leaves a deficiency of bonding electrons, the resulting non-classical carbocations contain bonds in which two electrons are shared between three nuclei. Protonated methane, CH5+, might be seen as the prototype of such species(1-3). But recent calculations(4,5) have suggested that all five C-H bonds are effectively equivalent and exchange dynamically very rapidly. It was therefore concluded(4) that CH5+ is a highly fluxional molecule without a definite structure, in which the representation in terms of three-centre two-electron bonding is misleading. Here we use a recently developed technique(6) to perform ab initio electronic structure calculations that include quantum effects of the nuclei. We find that, although there are prominent quantum-mechanical effects on the structure, including fluxionality, pseudo-rotations and hydrogen scrambling, the quantum ground state is nevertheless dominated on average by configurations in which an H-2 moiety is attached to a CH3 group forming a three-centre two-electron bond. To this extent, CH5+ should therefore resemble other carbonium ions.