By exploiting different sources for both reagents, the state-specific excitation function was deduced for the title reaction for the first time. It was found that for reactions with the ground state Cl(P-2(3/2)) atom, the rotation of the H-2 reagent has little effect on reactivity at low collision energies, but plays a beneficial role in promoting the reaction at higher E-c's; in contrast to a recent QCT prediction on the G3 surface. Evidence was presented for non-negligible reactivity from the spin-orbit excited Cl* (P-2(1/2)) atom. The ratio of the cross sections for a rotating H-2 to a nonrotating one appears to be larger for reaction with the ground state Cl than with the excited Cl*, sigma(j>0)/sigma(j=0)> sigma*(j>0)/sigma*(j=0).