Hydrogen kinetic isotope effect with values of alphaequivalent toln(k(H)/k(T))/ln(k(D)/k(T))>3.3 which are generally ascribed to quantum tunneling of hydrogen are shown to arise in O+HCI(DCl,TCl) reactions due to the effects of rotational excitation on the distribution of encounters with the critical dividing surface. At higher rotational excitations these distributions are shifted towards the regions of the critical dividing surface with low barrier energies which can lead to a large enhancement of the barrier crossing. This effect depends strongly on the hydrogen isotope involved in the reaction and, at some temperatures, gives rise to alpha much larger than 3.3. It can be readily seen that the effect should arise also in condensed molecular systems, due to internal rotations or other vibrations "perpendicular" to the reaction coordinate. (C) 2004 American Institute of Physics.