  The recent detection of gravitational waves by the LIGO/VIRGO collaboration
has allowed for the first tests of Einstein's theory in the extreme gravity
regime, where the gravitational interaction is simultaneously strong,
non-linear and dynamical. One such test concerns the rate at which the binaries
inspiral, or equivalently the rate at which the gravitational wave frequency
increases, which can constrain the existence of hairy black holes. This is
because black holes with scalar hair typically excite dipole radiation, which
in turn leads to a faster decay rate and frequency chirping. In this paper, we
present a mathematical proof that scalar hair is not sourced in vacuum,
spherically symmetric spacetimes when considering extensions of Einstein's
theory that break parity in gravity, focusing on dynamical Chern-Simons theory
as a particular toy model. This result implies that the observational
confirmation of the baldness of black holes cannot be used to constrain parity
violation in gravity, unless the black holes observed are also spinning.
