We present the third extension to the Very Long Baseline Array (VLBA) Calibrator Survey, containing 360 new sources not previously observed with Very Long Baseline Interferometry (VLBI). The survey, based on three 24 hour VLBA observing sessions, fills the areas on the sky above declination -45{deg} where the calibrator density is less than one source within a 4{deg} radius disk at any given direction. The positions were derived from astrometric analysis of the group delays determined at 2.3 and 8.6GHz frequency bands using the CALC/SOLVE software package. The VCS3 catalog of source positions, plots of correlated flux density versus length of projected baseline, and contour plots and FITS files of naturally weighted CLEAN images, as well as calibrated visibility function files, are available electronically from the Goddard Geodetic VLBI Group.