We explore chemically homogeneous evolution (CHE) as a formation channel for massive merging binary black holes (BBHs). We develop methods to include CHE in a rapid binary population synthesis code, Compact Object Mergers: Population Astrophysics and Statistics (compas), which combines realistic models of binary evolution with cosmological models of the star formation history of the Universe. For the first time, we simultaneously explore conventional isolated binary star evolution under the same set of assumptions. This approach allows us to constrain population properties and make simultaneous predictions about the gravitational-wave detection rates of BBH mergers for the CHE and conventional formation channels. The overall mass distribution of detectable BBHs is consistent with existing gravitational-wave observations. We find that the CHE channel may yield up to of all gravitational-wave detections of BBH mergers coming from isolated binary evolution.