The rate of the electron-exchange reaction between Cr(bipy)31+ and Cr(bipy)3 was measured in N,N-dimethylformamide by the ESR method, with the line-broadening procedure. The width of the partly-overlapped hyperfine lines was determined by comparing the observed spectrum with the computer-simulated one. The observed second-order rate constant was (1.5±0.4)×109 M−1 sec−1 at 25°C. When corrected for diffusion, this yielded the activation-controlled rate constant of 2.0×109 M−1 sec−1. It was pointed out that the rate constant obtained here was the largest of all those ever reported for the electron-exchange reactions in which the transition-metal complexes participated. The observed rate constant was in good agreement with the one calculated non-empirically according to the theory of R. A. Marcus. Although the value for the molecular radius must be chosen somewhat arbitrarily in applying this theory, the “good” radius was a reasonable one in view of the molecular geometry and dimensions of the reactants. The rate constant of the Heisenberg spin-exchange process was also determined to be 1.8×109 M−1 sec−1 at 25°C in the same solvent.