  The ab initio no-core shell model (NCSM) is extended to include a realistic
three-body interaction in calculations for p-shell nuclei. The NCSM formalism
is reviewed and new features needed in calculations with three-body forces are
discussed in detail. We present results of first applications to 6,7Li, 6He,
7,8,10Be, 10,11,12B, 12N and 10,11,12,13C using the Argonne V8' nucleon-nucleon
(NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction
(TNI). In addition to increasing the total binding energy, we observe a
substantial sensitivity in the low-lying spectra to the presence of the
realistic three-body force and an overall improvement in the level-ordering and
level-spacing in comparison to experiment. The greatest sensitivity occurs for
states where the spin-orbit interaction strength is known to play a role. In
particular, with the TNI we obtain the correct ground-state spin for 10,11,12B
and 12N, contrary to calculations with NN potentials only.
