In support of the NASA Deep Space 1 (DS1) mission to comet 19P/Borrelly, we obtained Hubble Space Telescope (HST) images and ultraviolet (UV) spectra of the comet near the time of the DS1 flyby in 2001 September. The HST data provide context information on 19P/Borrelly's circumnuclear dust environment, the rotational period and rotational phase of its nucleus, the H₂O and CS₂ production rates, the dust production rate, the dust reflectivity in the visible and mid-UV, and the time variability of these quantities around the time of the DS1 encounter. We derive average values of Q = (3.0 ± 0.6) × 10²⁸ molecules s^-1, [CS₂/H₂O] = (1.0 ± 0.3) × 10^-3, and Q_dust ≈ 240 kg s^-1. The corresponding dust-to-gas mass ratio is 0.24, but this is only a rough estimate because the dust production rate is uncertain by about an order of magnitude. The dust continuum was strongly reddened between 2400 and 3200 Å, and the Afρ value of 745 ± 15 cm near 6500 Å was ~2.5 times larger than the value near 2900 Å. The observed coma morphology consisted of a strong jet centered ~6° from the projected solar vector, one broad fan centered ~23° from the sunward direction, and another broad fan centered ~18° from the antisunward direction. The light curve of the optical continuum, as measured in target acquisition images, has an amplitude of ~40% in a square aperture that subtends 160 km at the comet; the rotational period could not be independently derived from the HST images but is consistent with the value of ~26 hr derived from HST observations in 1994 and ground-based images in 2000. The new HST data reveal a prominent offset in the emission peak of neutral gas molecules, and therefore in the peak column densities of gas in the coma, relative to the position of the cometary nucleus, which may be related to the offset in ion densities observed in situ by the DS1 Plasma Experiment for Planetary Exploration (PEPE) plasma spectrometer.