Electronic-structure calculations have shown that the six-center transition state for the concerted bond exchange among three hydrogen molecules lies -2 eV or more below the dissociation energy of the diatomic molecule. This suggests that solid hydrogen might undergo a high-pressure transition to form a new phase involving termolecular complexes. This possibility is examined by means of lattice-energy calculations employing semitheoretical pair potentials. Although uncertainties in the pair potentials prevent a definite conclusion, the results obtained for a range of potentials indicate that a phase comprising a “largely dissociated” form of the six-center transition state may be stable at pressures above a few hundred kilobars. This complex would exist only because repulsive forces from the neighboring units in the crystal environment prevent its dissociation.