The Cl + H-2 reaction is an important benchmark system in the study of chemical reaction dynamics that has always appeared to proceed via a direct abstraction mechanism, with no clear signature of reaction resonances. Here we report a high-resolution crossed-molecular beam study on the Cl + HD (v = 1, j = 0) -> DCl + H reaction (where v is the vibrational quantum number and j is the rotational quantum number). Very few forward scattered products were observed. However, two distinctive peaks at collision energies of 2.4 and 4.3 kilocalories per mole for the DCl (v' = 1) product were detected in the backward scattering direction. Detailed quantum dynamics calculations on a highly accurate potential energy surface suggested that these features originate from two very short-lived dynamical resonances trapped in the peculiar H-DCl (v' = 2) vibrational adiabatic potential wells that result from chemical bond softening. We anticipate that dynamical resonances trapped in such wells exist in many reactions involving vibrationally excited molecules.