The specifics of how galaxies form from, and are fuelled by, gas from the intergalactic medium remain uncertain. Hydrodynamic simulations suggest that 'cold accretion flows'--relatively cool (temperatures of the order of 10(4) kelvin), unshocked gas streaming along filaments of the cosmic web into dark-matter halos--are important. These flows are thought to deposit gas and angular momentum into the circumgalactic medium, creating disk- or ring-like structures that eventually coalesce into galaxies that form at filamentary intersections. Recently, a large and luminous filament, consistent with such a cold accretion flow, was discovered near the quasi-stellar object QSO UM287 at redshift 2.279 using narrow-band imaging. Unfortunately, imaging is not sufficient to constrain the physical characteristics of the filament, to determine its kinematics, to explain how it is linked to nearby sources, or to account for its unusual brightness, more than a factor of ten above what is expected for a filament. Here we report a two-dimensional spectroscopic investigation of the emitting structure. We find that the brightest emission region is an extended rotating hydrogen disk with a velocity profile that is characteristic of gas in a dark-matter halo with a mass of 10(13) solar masses. This giant protogalactic disk appears to be connected to a quiescent filament that may extend beyond the virial radius of the halo. The geometry is strongly suggestive of a cold accretion flow.