The kinetics of the reaction of chlorine atoms with C2H4 and C2D4 have been studied near the low-pressure limit at 1 Torr total pressure and room temperature using two independent techniques. A fast flow discharge system (FFDS) was used to follow the decay of Cl in the presence of a great excess of either C2H4 or C2D4 in He as the carrier gas. Atomic chlorine was generated from the rapid reaction F + HCl --> Cl + HF and detected using resonance fluorescence at 135 nm. In relative rate (RR) studies, Cl-2 was photolyzed to generate chlorine atoms in a mixture of the two organics in N-2 or He as the bath gas, and the loss of C2H4 or C2D4 relative to CH4 was followed using GC-FID. The rate constant for the Cl + C2D4 reaction determined using the FFDS was (3.3 +/- 0.6) x 10(-13) cm(3) molecule(-1) s(-1) and for the Cl + C2D4 reaction was (10.0 +/-1.9) x 10(-13) cm(3) molecule(-1) s(-1), a factor of 3.0 +/-0.8 times larger than that for the C2H4 reaction (all errors are +/-2 sigma). The Cl + C2H4 rate constant determined using the RR method was (2.9 +/- 0.4) x 10(-13) cm(3) molecule(-1) s(-1), based on k(Cl+CH4) = (1.0 +/- 0.1) x 10(-13) cm(3) molecule(-1) s(-1). The rate constant for Cl + C2D4 was (7.8 +/- 1.6) x 10(-13) cm(3) molecule(-1) s(-1), a factor of 2.7 +/- 0.7 times larger than that for C2H4, in excellent agreement with the FFDS results. This strong inverse kinetic isotope effect is shown to be in excellent agreement with what would be predicted from unimolecular reaction rate theory and their reverse recombination processes.