We identify 3,113 highly variable objects in 7,200 square degrees of the Palomar-QUEST Survey, which each varied by more than 0.4 magnitudes simultaneously in two broadband optical filters on timescales from hours to roughly 3.5 years. The primary goal of the selection is to find blazars by their well-known violent optical variability. Because most known blazars have been found in radio and/or X-ray wavelengths, a sample discovered through optical variability may have very different selection effects, elucidating the range of behavior possible in these systems. A set of blazars selected in this unusual manner will improve our understanding of the physics behind this extremely variable and diverse class of AGN. The object positions, variability statistics, and color information are available using the Palomar-QUEST CasJobs server. The time domain is just beginning to be explored over large sky areas; we do not know exactly what a violently variable sample will hold. About 20% of the sample has been classified in the literature; over 70% of those objects are known or likely AGN. The remainder largely consists of a variety of variable stars, including a number of RR Lyrae and cataclysmic variables.