  The standard model of cosmology is underpinned by the assumption of the
statistical isotropy of the Universe. Observations of the cosmic microwave
background, galaxy distributions, and supernovae, among other media, support
the assumption of isotropy at scales $\gtrsim 100$\,Mpc. The recent detections
of gravitational waves from merging stellar-mass binary black holes provide a
new probe of anisotropy; complementary and independent of all other probes of
the matter distribution in the Universe. We present an analysis using a
spherical harmonic model to determine the level of anisotropy in the first
LIGO/Virgo transient catalog. We find that the ten binary black hole mergers
within the first transient catalog are consistent with an isotropic
distribution. We carry out a study of simulated events to assess the prospects
for future probes of anisotropy. Within a single year of operation,
third-generation gravitational-wave observatories will probe anisotropies with
an angular scale of $\sim36^\circ$ at the level of $\lesssim0.1\%$.
