The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator alpha-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of alpha-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.