This paper describes how chirp stimuli can be used to compensate for the cochlear traveling wave delay in recordings of the ASSR (rate: ~90/s). The temporal dispersion in the cochlea is given by the traveling time, which in this study is estimated from latency-frequency functions obtained from (1) a cochlear model, (2) tone-burst auditory brain stem response ABR-latencies, and (3) derived-band ABR-latencies. These latency-frequency functions are assumed to reflect the group delay of a linear system that modifies the phase spectrum of the applied stimulus. On the basis of this assumption, three chirps are constructed and evaluated in normal-hearing subjects (N = 49). The ASSR to these chirps and to a click stimulus are compared at two levels of stimulation viz. 30 and 50 dB nHL and at a rate of 90/s. The chirps give shorter detection time and higher signal-to-noise ratio than the click. The shorter detection time obtained by the chirps is equivalent to an increase in stimulus level of 20 dB or more. The chirp based on the derived-band ABR-latencies appears to be the most efficient of the three chirps tested here. Overall, the results indicate that a chirp is a more efficient stimulus than a click for the recording of the ASSR in normal-hearing adults using transient sounds at a high rate of stimulation.