  As gravitational wave detectors improve, observations of black hole (BH)
mergers will provide the joint distribution of their masses and spins. This
will be a critical benchmark to validate formation scenarios. Merging binary
BHs formed through isolated binary evolution require both components to be
stripped of their hydrogen envelopes before core-collapse. The rotation rates
of such stripped stars are constrained by their surface critical rotation,
restricting their angular momentum content at core-collapse. We use stripped
star models at low metallicities ($Z_\odot/10$, $Z_\odot/50$ and $Z_\odot/250$)
to determine the spins of BHs produced by critically rotating stellar
progenitors. To study how such progenitors can arise, we consider their
formation through chemically homogeneous evolution (CHE). We use a
semianalytical model to study the final spins of CHE binaries, and compare our
results against available detailed population synthesis models. We find that
above BH masses of $\simeq 25M_\odot$, the dimensionless spin of critically
rotating stripped stars ($a = Jc/(GM^2$)) is below unity. This results in an
exclusion region at high chirp masses and effective spins that cannot be
populated by binary evolution. CHE can produce binaries where both BHs hit this
limit, producing a pile-up at the boundary of the excluded region. Highly
spinning BHs arise from very low-metallicity CHE systems with short delay
times, which merge at higher redshifts. On the other hand, the contribution of
CHE to merging binary BHs in the third observing run of the LVK collaboration
is 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 and
runtime, the fourth observing run of the LVK collaboration can potentially
place constraints on the high spin population and the existence of a limit set
by critical rotation.
