  We present the results of an exploratory Lattice QCD calculation of
three-baryon systems through a high-statistics study of one ensemble of
anisotropic clover gauge-field configurations with a pion mass of m_\pi ~ 390
MeV. Because of the computational cost of the necessary contractions, we focus
on correlation functions generated by interpolating-operators with the quantum
numbers of the $\Xi^0\Xi^0 n$ system, one of the least demanding three baryon
systems in terms of the number of contractions. We find that the ground state
of this system has an energy of E_{\Xi^0\Xi^0n}= 3877.9\pm 6.9\pm 9.2\pm3.3 MeV
corresponding to an energy-shift due to interactions of \delta
E_{\Xi^0\Xi^0n}=E_{\Xi^0\Xi^0n}-2M_{\Xi^0} -M_n=4.6\pm 5.0\pm 7.9\pm 4.2 MeV.
There are a significant number of time-slices in the three-baryon correlation
function for which the signal-to-noise ratio is only slowly degrading with
time. This is in contrast to the exponential degradation of the signal-to-noise
ratio that is observed at larger times, and is due to the suppressed overlap of
the source and sink interpolating-operators that are associated with the
variance of the three-baryon correlation function onto the lightest eigenstates
in the lattice volume
  (mesonic systems). As one of the motivations for this area of exploration is
the calculation of the structure and reactions of light nuclei, we also present
initial results for a system with the quantum numbers of the triton (pnn). This
present work establishes a path to multi-baryon systems, and shows that Lattice
QCD calculations of the properties and interactions of systems containing four
and five baryons are now within sight.
