We investigate the statistics of single-mode delay times of waves reflected from a disordered waveguide in the presence of wave localization. The distribution of delay times is qualitatively different from the distribution in the diffusive regime, and sensitive to coherent backscattering: The probability of finding small delay times is enhanced by a factor close to sqrt[2] for reflection angles near the angle of incidence. This dynamic effect of coherent backscattering disappears in the diffusive regime.