  Understanding the volume dependence of the triton binding energy is an
important step towards lattice simulations of light nuclei. We calculate the
triton binding energy in a finite cubic box with periodic boundary conditions
to leading order in the pionless effective field theory. Higher order
corrections are estimated and the proper renormalization of our results is
verified explicitly. We present results for the physical triton as well as for
the pion-mass dependence of the triton spectrum near the ``critical'' pion
mass, Mpi_c ~ 197 MeV, where chiral effective field theory suggests that the
nucleon-nucleon scattering lengths in the singlet- and triplet-channels diverge
simultaneously. An extension of the Luescher formula to the three-body system
is implicit in our results.
