We report CCD photometry of 2060 Chiron from two apparitions. A partial light curve was obtained in 1985 January, when the object was intrinsically fainter ( Hv = 6.84) than it has ever been seen before or since. Nonetheless, there was some evidence for cometary activity even then; the bare nucleus may be fainter still. A complete light curve was obtained over 10 hr on 1991 January 08. Similar in character to the 1990 lightcurve of J. X. Luu and D.C. Jewitt (1990, Astron. J. 100, 913-932), it differed in three important respects. The amplitude was lower (0.04 mag), the mean brightness level was higher than recent trends would predict (mean HR = 5.65), and the mean remained constant over 1 1/2 rotations to within better than 0.005 mag. The light curve shows reproducible structure of relatively high-frequency (̃15-min time scale), formerly attributed to noise. These features repeat within the night and also may be discerned in light curves dating back to 1986 (S. J. Bus, E. Bowell, A. W. Harris, and A. V. Hewitt, 1989, Icarus 77, 223-238). We believe this structure to be evidence that Chiron is more aspherical (faceted?) than the small-amplitude lightcurve otherwise implies. The rotational lightcurve now is sufficiently well-characterized that it is no longer necessary to obtain data over a complete rotation to monitor the so-called "outburst" behavior of the object. We hope that this will encourage observers to study the cometary behavior of Chiron on time scales of days to weeks. An updated mean synodic period of 5.917813 ± 0.000007 hr has been derived, and a revised nucleus + coma photometric model is constructed using the new data. The results of this model, along with the observed rapid "dropouts" in the rotational lightcurve, are together taken as evidence for a relatively low-obliquity viewing geometry over the past decade.