Recent advances in the isolation and stacking of monolayers of van der Waals materials have provided approaches for the preparation of quantum materials in the ultimate two-dimensional limit1,2. In van der Waals heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice3. It is widely recognized that the moiré superlattice can modulate the electronic band structure of the material and lead to transport properties such as unconventional superconductivity4 and insulating behaviour driven by correlations5-7; however, the influence of the moiré superlattice on optical properties has not been investigated experimentally. Here we report the observation of multiple interlayer exciton resonances with either positive or negative circularly polarized emission in a molybdenum diselenide/tungsten diselenide (MoSe2/WSe2) heterobilayer with a small twist angle. We attribute these resonances to excitonic ground and excited states confined within the moiré potential. This interpretation is supported by recombination dynamics and by the dependence of these interlayer exciton resonances on twist angle and temperature. These results suggest the feasibility of engineering artificial excitonic crystals using van der Waals heterostructures for nanophotonics and quantum information applications.