  We calculate in (two-loop) chiral perturbation theory the local NN-potentials
generated by the three-pion exchange diagrams proportional to g_A^4 and g_A^6.
Surprisingly, we find that the total isoscalar central $3\pi$-exchange
potential vanishes identically. The individually largest $3\pi$-exchange
potentials are of isoscalar spin-spin, isovector central and isoscalar tensor
type. For these potentials simple analytical expressions can be given. The
strength of these dominant $3\pi$-exchange potentials at r=1.0 fm is 4.6 MeV,
2.9 MeV and 1.4 MeV, respectively. Furthermore, we observe that the spin-spin
and tensor potentials due to the diagrams proportional to g_A^6 do not exist in
the infinite nucleon mass limit.
