  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 $\gamma$-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.
