Nuclear decay induced Cl-37 ion desorption from the electron capture decay Ar-37-->Cl-37+nu is reported for the first time. A mixture of one part Ar-36 and approximately 5X10(-5) parts Ar-37 (Ar-36/37) is physisorbed on a gold-plated Si wafer kept at 16 K under ultrahigh vacuum conditions. The time of flight (TOF) of recoiled Cl-37 ions is measured using coincidence techniques. The observed kinetic energy distribution of the Cl-37 ions is approximately Gaussian in shape, with a maximum at almost-equal-to 9.0 eV and a full width at half-maximum of approximately 3 eV. Considering the binding energy of physisorbed Ar-37 is approximately 80 meV, the 9-eV peak energy compares well with that of the gas-phase value, where conservation of the energy and momentum fixes the kinetic energy of Cl-37 ions at 9.54 eV. Using a combination of TOF and retarding field energy analysis, the charge states of detected ions for 1 ML (monolayer) of Ar-36/37 are determined as 53%+1e, 21%+2e, and 26%+ne, where n greater-than-or-equal-to 3. The fraction of decaying Ar-37 atoms which emerge from the surface as positive Cl-37 ions is found to be 10%. Finally, a strong charge exchange reaction between a Cl-37 ion and near-neighbor atoms causes a Coulomb explosion within the multilayers, increasing the kinetic energy of desorbing ions by as much as approximately 7 eV.