In binary black hole mergers from isolated binary-star evolution, both black holes are from progenitor stars that have lost their hydrogen-rich envelopes by binary mass transfer. Envelope stripping is known to affect the pre-supernova core structures of such binary-stripped stars and thereby their final fates and compact remnant masses. In this paper, we show that binary-stripped stars give rise to a bimodal black hole mass spectrum with characteristic black hole masses of about 9 M ⊙ and 16 M ⊙ across a large range of metallicities. The bimodality is linked to carbon and neon burning becoming neutrino dominated, which results in interior structures that are difficult to explode and likely lead to black hole formation. The characteristic black hole masses from binary-stripped stars have corresponding features in the chirp-mass distribution of binary black hole mergers: peaks at about 8 and 14 M ⊙ and a dearth in between these masses. Current gravitational-wave observations of binary black hole mergers show evidence for a gap at 10–12 M ⊙ and peaks at 8 and 14 M ⊙ in the chirp-mass distribution. These features are in agreement with our models of binary-stripped stars. In the future, they may be used to constrain the physics of late stellar evolution and supernova explosions and may even help measure the cosmological expansion of the universe.