We propose to build the Very Energetic Radiation Imaging Telescope Array System (VERITAS), an array of seven 10m aperture optical reflectors for gamma-ray astronomy in the 50GeV to 50TeV energy range. These atmospheric Cherenkov telescopes will use the imaging concept developed by the Whipple Observatory Gamma-Ray Collaboration and used to detect the first galactic and extragalactic sources of TeV gamma-rays but will achieve an order of magnitude better sensitivity and a significant reduction in energy threshold. The new telescopes will improve upon the design of the existing Whipple Observatory 10m telescope. Each telescope will have a tessellated 10m mirror and long focal length (12m) with the optical design optimized for good angular resolution, a large field of view, and minimum wavefront distortion. Each telescope camera will have 499 pixels covering a 3.5 field of view with 0.15resolution. The detectors and camera electronics will use the most advanced technology currently available. The array will have an effective collection area in excess of 100,000m2 at energies above 1TeV. VERITAS will be located in southern Arizona where it will take advantage of the existing infrastructure of the Whipple Observatory. With stereoscopic imaging, the array will achieve unprecedented angular resolution, energy resolution and background rejection over three decades of energy. The primary scientific objectives of VERITAS will be the study of active galactic nuclei, supernova remnants, pulsars, and gamma-ray bursts and the search for new astrophysical sources. The minimum detectable flux sensitivity will be 0.5% of the Crab Nebula at 200GeV, a factor of 20 improvement over the most sensitive telescopes currently operating in this energy range. The angular resolution (<0.05) will be sufficient to identify a number of the unidentified sources detected by EGRET on the Compton Gamma Ray Observatory. VERITAS provides a unique combination of large collection area, low background, and good energy resolution. It will effectively complement GLAST, the next major high energy gamma-ray telescope in space; together they may solve the problem of the origin of the cosmic radiation as well as probing fundamental questions in physics and cosmology. The capital cost of VERITAS is $21M and it can be built in five years.