In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods for nuclear physics to test to what extent chiral effectice field theory framework impacts our knowledge of few- and many-body systems. We present quantum Monte Carlo calculations of light nuclei based on local chiral two-nucleon interactions constructed by our group in a previous work in conjuction with a chiral three-nucleon force fitted to bound- and scattering-state observables in the three-body sector. These results lead to predictions for the energy levels and level ordering of nuclei in the mass range A = 4-12, accurate to <= 2% of the binding energy, in very satisfactory agreement with experimental data.