MPW1K/6-31 + G(d,p) calculations which include the effects of small curvature tunneling find that, around room temperature, thermally activated tunneling dominates the 1,5-hydrogen shift reactions of 1,3-cyclopentadiene (2a) and 5-methyl-1,3-cyclopentadiene (2c). The calculated temperature dependence of the H/D kinetic isotope effect (KIE) for the latter rearrangement agrees well with experimental measurements that were published nearly 40 years ago. It is argued that the experimental KIEs provide prima facie evidence for tunneling in this reaction. The calculations also predict that it should be possible, at least in principle, to confirm this conclusion by observing curvature in the Arrhenius plot for the rearrangement of 2c.