We explore the possibility of detecting baryon acoustic oscillations (BAO) solely from gravitational wave (GW) observations of binary neutron star mergers with third-generation (3G) GW detectors such as the Cosmic Explorer and the Einstein Telescope. These measurements would provide a new independent probe of cosmology. The detection of the BAO peak with current-generation GW detectors (solely from GW observations) is not possible because i) unlike galaxies, the GW mergers are poorly localized, and ii) there are not enough merger events to probe the BAO length scale. With the 3G GW detector network, it is possible to observe 1/4 (1000) binary neutron star mergers per year that are localized well within one square degree in the sky for redshift z ≤ 0.3. We show that 3G observatories will enable precision measurements of the BAO feature in the large-scale two-point correlation function; the effect of BAO can be independently detected at different redshifts, with a log-evidence ratio of 1/423, 17, or 3, favoring a model with a BAO peak at redshift of 0.2, 0.25, or 0.3, respectively, using a redshift bin corresponding to a shell of thickness 150h -1 Mpc. © 2022. The Author(s). Published by the American Astronomical Society.