We have measured the velocity of the Local Group with respect to an inertial frame defined by the 119 Abell and Abell, Corwin, & Olowin (ACO, Cat. <VII/110A>) clusters contained within 15000km/s. The observations consist of a full-sky peculiar velocity survey with an effective depth ranging from 8000 to 11000km/s, depending on how the observations are weighted with redshift. This is the deepest peculiar velocity survey yet conducted. Clusters are selected by heliocentric redshift, and the sample is volume-limited. We use the Hoessel (1980ApJ...241..493H) relationship between the metric luminosities of the brightest clusters galaxies (BCGs) and the slope of their brightness profiles as the distance indicator. The Cousins R-band luminosity within a metric radius of 10h^-1^kpc yields a typical distance error of 16% for a single BCG.