The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl + XCl → XCl + Cl (X=H, D, Mu). For the Cl + HCl reaction, the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory. And the RPMD results also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics. The most novel finding is there is a double peak in Cl + MuCl reaction near the transition state, leaving a free energy well. It comes from the mode softening of the reaction system at the peak of the potential energy surface. Such an explicit free energy well suggests strongly there is an observable resonance. And for the Cl + DCl reaction, the RPMD rate coefficient again gives very accurate results comparing with experimental values. The only exception is at the temperature of 312.5 K, at this temperature, results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value, which indicates experimental or potential energy surface deficiency.