  A major goal of nuclear theory is to explain the spectra and stability of
nuclei in terms of effective many-body interactions amongst the nucleus'
constituents-the nucleons, i.e., protons and neutrons. Such an approach,
referred to below as the basic model of nuclear theory, is formulated in terms
of point-like nucleons, which emerge as effective degrees of freedom, at
sufficiently low energy, as a result of a decimation process, starting from the
fundamental quarks and gluons, described by Quantum Chromodynamics (QCD). A
systematic way to account for the constraints imposed by the symmetries of QCD,
in particular chiral symmetry, is provided by chiral effective field theory, in
the framework of a low-energy expansion. Here we show, in quantum Monte Carlo
calculations accurate to $\leq\!2\%$ of the binding energy, that two- and
three-body chiral interactions fitted {\sl only} to bound- and scattering-state
observables in, respectively, the two- and three-nucleon sectors, lead to
predictions for the energy levels and level ordering of nuclei in the mass
range $A\,$=$\,$4-12 in very satisfactory agreement with experimental data. Our
findings provide strong support for the fundamental assumptions of the basic
model, and pave the way to its systematic application to the electroweak
structure and response of these systems as well as to more complex nuclei.
