We investigate the effects of wave localization on the delay time � (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered waveguide. Localization results in a separation �=�+�� of the delay time into two independent but equivalent contributions, associated to the left and right end of the waveguide. For N=1 propagating modes, � and �� are identical to half the reflection delay time of each end of the waveguide. In this case the distribution function P(�) in an ensemble of random disorder can be obtained analytically. For N>1 propagating modes the distribution function can be approximated by a simple heuristic modification of the single-channel problem. We find a strong correlation between channels with long reflection delay times and the dominant transmission channel.