  We present a shell model calculation for the beta decay of 14-C to the 14-N
ground-state, treating the relevant nuclear states as two 0p-holes in an 16-O
core. Employing the universal low-momentum nucleon-nucleon potential V(low-k)
only, one finds that the Gamow-Teller matrix element is too large to describe
the known (very long) lifetime of 14-C. As a novel approach to the problem, we
invoke the chiral three-nucleon force (3NF) at leading order and derive from it
a density-dependent in-medium NN interaction. Including this effective
in-medium NN interaction, the Gamow-Teller matrix element vanishes for a
nuclear density close to that of saturated nuclear matter. The genuine
short-range part of the three-nucleon interaction plays a particularly
important role in this context, since the medium modifications to the pion
propagator and pion-nucleon vertex (due to the long-range 3NF) tend to cancel
out in the relevant observable. We discuss also uncertainties related to the
off-shell extrapolation of the in-medium NN interaction. Using the off-shell
behavior of V(low-k) as a guide, we find that these uncertainties are rather
small.
