  Within pNRQCD we compute the masses of spin-averaged triply heavy baryons
using the now-available NNLO pNRQCD potentials and three-body variational
approach. We focus in particular on the role of the purely three-body
interaction in perturbation theory. This we find to be reasonably small and of
the order 25 MeV Our prediction for the Omega_ccc baryon mass is 4900(250) in
keeping with other approaches. We propose to search for this hitherto
unobserved state at B factories by examining the end point of the recoil
spectrum against triple charm.
