The pattern of occurrence of isolated action potentials recorded from the cat's auditory nerve fiber is modeled over short time scales as a renewal process. For counting times greater than one second, the count variance-to-mean ratio grows as a power of the counting time. Such behavior is consistent with a renewal process driven by a fractal random waveform process (1/f-type spectrum). Based on 108 recordings each 600 seconds long, we conclude that the presence of the fractal noise is independent of characteristic frequency and stimulus level. This noise appears to originate in the cochlear inner hair cells. We measured the low frequency power of the fractal noise, finding its coefficient of variation to decrease as firing rate increases. Such behavior is consistent with multiplicative random variations in the permeability of the hair cell membrane to neuro-transmitter and also with increased level discrimination acuity at high stimulus levels.