According to quantum theory, adjacent particles of condensed systems may exhibit quantum interference and/or correlation phenomena being caused by interparticle interactions. Here we present, for the first time, direct experimental evidence for short-lived quantum entanglement of protons of C-H bonds. Neutron Compton scattering results from solid polystyrene reveal that, in the sub-femtosecond time scale, the measured cross-section density of the protons is "anomalously" reduced by ca. 20%. A first-principles theoretical treatment of this effect is given, which is based on the well-known van Hove formalism, and also takes explicitly into account quantum entanglement of protonic states and its decoherence. Besides its fundamental physical character, the effect may have considerable chemical and biological applications, and also be of technical importance, e.g., for the engineering of some neutron moderators.