Transport experiments in twisted bilayer graphene have revealed multiple superconducting domes separated by correlated insulating states^1–5. These properties are generally associated with strongly correlated states in a flat mini-band of the hexagonal moiré superlattice as was predicted by band structure calculations^6–8. Evidence for the existence of a flat band comes from local tunnelling spectroscopy^9–13 and electronic compressibility measurements¹⁴, which report two or more sharp peaks in the density of states that may be associated with closely spaced Van Hove singularities. However, direct momentum-resolved measurements have proved to be challenging¹⁵. Here, we combine different imaging techniques and angle-resolved photoemission with simultaneous real- and momentum-space resolution (nano-ARPES) to directly map the band dispersion in twisted bilayer graphene devices near charge neutrality. Our experiments reveal large areas with a homogeneous twist angle that support a flat band with a spectral weight that is highly localized in momentum space. The flat band is separated from the dispersive Dirac bands, which show multiple moiré hybridization gaps. These data establish the salient features of the twisted bilayer graphene band structure.