  Binary black holes on quasicircular orbits with spins aligned with their
orbital angular momentum have been testbeds for analytic and numerical
relativity for decades, not least because symmetry ensures that such
configurations are equilibrium solutions to the spin-precession equations. In
this work, we show that these solutions can be unstable when the spin of the
higher-mass black hole is aligned with the orbital angular momentum and the
spin of the lower-mass black hole is anti-aligned. Spins in these
configurations are unstable to precession to large misalignment when the binary
separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{\chi_1} \pm \sqrt{q
\chi_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is
the mass ratio, and $\chi_1$ ($\chi_2$) is the dimensionless spin of the more
(less) massive black hole. This instability exists for a wide range of spin
magnitudes and mass ratios and can occur in the strong-field regime near
merger. We describe the origin and nature of the instability using recently
developed analytical techniques to characterize fully generic spin precession.
This instability provides a channel to circumvent astrophysical spin alignment
at large binary separations, allowing significant spin precession prior to
merger affecting both gravitational-wave and electromagnetic signatures of
stellar-mass and supermassive binary black holes.
