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As gravitational wave detectors improve, observations of black hole (BH)mergers will provide the joint distribution of their masses and spins. Thiswill be a critical benchmark to validate formation scenarios. Merging binaryBHs formed through isolated binary evolution require both components to bestripped of their hydrogen envelopes before core-collapse. The rotation ratesof such stripped stars are constrained by their surface critical rotation,restricting their angular momentum content at core-collapse. We use strippedstar models at low metallicities ($Z_\odot/10$, $Z_\odot/50$ and $Z_\odot/250$)to determine the spins of BHs produced by critically rotating stellarprogenitors. To study how such progenitors can arise, we consider theirformation through chemically homogeneous evolution (CHE). We use asemianalytical model to study the final spins of CHE binaries, and compare ourresults against available detailed population synthesis models. We find thatabove BH masses of $\simeq 25M_\odot$, the dimensionless spin of criticallyrotating stripped stars ($a = Jc/(GM^2$)) is below unity. This results in anexclusion region at high chirp masses and effective spins that cannot bepopulated by binary evolution. CHE can produce binaries where both BHs hit thislimit, producing a pile-up at the boundary of the excluded region. Highlyspinning BHs arise from very low-metallicity CHE systems with short delaytimes, which merge at higher redshifts. On the other hand, the contribution ofCHE to merging binary BHs in the third observing run of the LVK collaborationis expected to be dominated by systems with low spins ($\chi_\mathrm{eff}<0.5$)which merge near redshift zero. Owing to its higher projected sensitivity andruntime, the fourth observing run of the LVK collaboration can potentiallyplace constraints on the high spin population and the existence of a limit setby critical rotation.

An upper limit on the spins of merging binary black holes formed through binary evolution