We present observations of the evolution of a prominent spiral jet in the inner coma of comet Hale-Bopp (1995 O1). The observations, taken with the 82 cm IAC-80 telescope at the Teide Observatory, were made on 1995 August 25, 27, 28, and 31, and on September 4--7, as part of an ongoing program of monitoring the comet in Tenerife. The jet is observed to show a nearly, but not completely, constant position angle over the two weeks of observation. Although it is generally assumed that the jet is a dust event, some aspects of the morphology and behavior mean that the hypothesis that it is a gas jet cannot be ruled out. No single hypothesis is thought to be completely satisfactory. Between our first detection of the jet on August 25 and its disappearance on September 7, we see the point of inflection within the jet expand away from the nucleus at a highly constant velocity. At the same time, the jet fades considerably. This jet event seems different from others that have been observed later because the collimation of the beam is very tight, rather than the highly wound spiral structure shown by some later jets.