Naturally occurring chorus emissions are a class of electromagnetic waves found in the space environments of the Earth and other magnetized planets. They play an essential role in accelerating high-energy electrons forming the hazardous radiation belt environment. Chorus typically occurs in two distinct frequency bands separated by a gap. The origin of this two-band structure remains a 50-year old question. Here we report, using NASA's Van Allen Probe measurements, that banded chorus waves are commonly accompanied by two separate anisotropic electron components. Using numerical simulations, we show that the initially excited single-band chorus waves alter the electron distribution immediately via Landau resonance, and suppress the electron anisotropy at medium energies. This naturally divides the electron anisotropy into a low and a high energy components which excite the upper-band and lower-band chorus waves, respectively. This mechanism may also apply to the generation of chorus waves in other magnetized planetary magnetospheres.