Gamma rays with energy above 10 GeV interact with optical-UV photons resulting in pair production. Therefore, a large sample of high redshift sources of these gamma rays can be used to probe the extragalactic background starlight (EBL) by examining the redshift dependence of the attenuation of the flux above 10 GeV. GLAST, the next generation high-energy gamma-ray telescope, will have the unique capability to detect thousands of gamma-ray blazars to redshifts of at least z=4, with sufficient angular resolution to allow identification of a large fraction of their optical counterparts. By combining established models of the gamma-ray blazar luminosity function, two different calculations of the high energy gamma-ray opacity due to EBL absorption, and the expected GLAST instrument performance to produce simulated fluxes and redshifts for the blazars that GLAST would detect, we demonstrate that these gamma-ray blazars have the potential to be a highly effective probe of the optical-UV EBL.