  We show that gravitational Chern-Simons corrections, associated with the
sigma-model anomaly on the M5-brane world-volume, can resolve the singularity
of the M2-brane solution with Ricci-flat, special holonomy transverse space. We
explicitly find smooth solutions in the cases when the transverse space is a
manifold of Spin(7) holonomy and SU(4) holonomy. We comment on the consequences
of these results for the holographically related three-dimensional theories
living on the world volume of a stack of such resolved M2-branes.
