The laboratory energy distribution of H+ from the dissociation of H3+ in low-keV H3+-He collisions is measured at a 0\ifmmode^\circ\else\textdegree\fi{} laboratory angle. An inelastic energy loss of Q=26\ifmmode\pm\else\textpm\fi{}2 eV has been determined for the excited states of H3+ that produce low-energy protons upon dissociation. An approximate projectile-frame energy distribution of H+ is also presented. Our results suggest that the near-zero projectile-frame energy protons are produced by either an electronic singlet excitation of the ground state of H3+ to a distribution of 2 E1\ensuremath{'}, 1 E1\ensuremath{''}, and 2 A12\ensuremath{''}, or as an alternative mechanism, a triplet excitation of H3+ to 1 E3\ensuremath{'} accompanied by a simultaneous triplet excitation of the He target. In either case, the near-zero energy protons are produced by a three-body dissociation of the excited (H3+)*. In the case of the triplet excitation, there are no long-range correlations for the motion of the neutral H atoms. For the singlet excitation, the neutral H atoms' motion is correlated and the angle between them is near 180\ifmmode^\circ\else\textdegree\fi{}. The effects of the long-range nature of the total potential between the fragments is discussed in terms of the hyperspherical coordinates.