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Rate constants for dissociative electron attachment to Cl2 have been measured from 300 to 1100 K in a high-temperature flowing-afterglow Langmuir-probe apparatus. R-matrix calculations have been carried out which compare well with the present measurements with possible deviation at the highest temperatures. The attachment rate constants do not show Arrhenius behavior. The temperature dependence of the calculated rate constants for successive vibrational levels provides insight as to this behavior. While the lowest vibrational level of Cl2 dominates attachment at low temperatures, the rate constant is not flat with temperature because of the p-wave character of the attachment process. The non-Arrhenius behavior is due to a conflict between the increase in attachment cross section with vibrational level (temperature) and the decline in the cross section with electron energy above 50 meV.