  The specific mass shift in the electron affinity between ^{35}Cl and ^{37}Cl
has been determined by tunable laser photodetachment spectroscopy to be
-0.51(14) GHz. The isotope shift was observed as a difference in the onset of
the photodetachment process for the two isotopes. In addition, the electron
affinity of Cl was found to be 29138.59(22) cm^{-1}, giving a factor of 2
improvement in the accuracy over earlier measurements. Many-body calculations
including lowest-order correlation effects demonstrates the sensitivity of the
specific mass shift and show that the inclusion of higher-order correlation
effects would be necessary for a quantitative description.
