The first atmospheric Cherenkov telescope of VERITAS (the Very Energetic Radiation Imaging Telescope Array System) has been in operation since February 2005. We present here a technical description of the instrument and a summary of its performance. The calibration methods are described, along with the results of Monte Carlo simulations of the telescope and comparisons between real and simulated data. The analysis of TeV γ-ray observations of the Crab Nebula, including the reconstructed energy spectrum, is shown to give results consistent with earlier measurements. The telescope is operating as expected and has met or exceeded all design specifications.