The chaotic light signals generated by an external cavity semiconductor laser have been experimentally demonstrated to extract fast random numbers. However, the photon round-trip time in the external cavity can cause the occurrence of the periodicity in random sequences. To overcome it, the exclusive-or operation on corresponding random bits in samples of the chaotic signal and its time-delay signal from a chaotic laser is required. In this scheme, the proper selection of delay length is a key issue. By doing a large number of experiments and theoretically analyzing the interplay between the Runs test and the threshold value of the autocorrelation function, we find when the corresponding delay time of autocorrelation trace with the correlation coefficient of less than 0.007 is considered as the delay time between the chaotic signal and its time-delay signal, streams of random numbers can be generated with verified randomness.