Many researchers have reported that narrowband hiss emissions are simultaneously present with ELF chorus emissions outside of the plasmasphere. In data from the SCATHA satelite, chorus emissions are often observed to start at frequencies that are within a hiss band. Hiss band spectra averaged for 6.4 s with a resolution of 5 Hz are very smooth. Relative maxima are typically less than 2 dB above adjacent minima. Spectra obtained on a 200-ms sample show large variations in amplitude between adjacent bins with relative maxima 10-15 dB above adjacent minima. Electrons in a narrow range of energies and pitch angles can be organized in phase by the Doppler-shifted cyclotron resonance with the larger-amplitude spectral components in the hiss band. The bandwidth of the cyclotron resonance is found to be sufficiently narrow so that the electrons are not dephased by waves in adjacent portions of the highly structured spectrum. The amplitude of the hiss is sufficient to significantly phase bunch the electrons in the calculated interaction time. The chorus emission is then generated as the phase-bunched electron moved adiabatically along the geomagnetic field line. No evidence for monochromatic input waves such as power line harmonic radiation is found in the SCATHA data within the hiss bands from which chorus is observed to be triggered. This mechanism can also account for the chorus emission detected at frequencies above a hiss band in the Jovian magnetosphere.