The centaur (2060) Chiron exhibits outgassing behaviour and possibly hosts a ring system. On 2011 November 29, Chiron occulted a fairly bright star (R~15 mag) as observed from the 3m NASA Infrared Telescope Facility (IRTF) on Mauna Kea and the 2-m Faulkes Telescope North (FTN) at Haleakala. Data were taken as visible wavelength images and simultaneous, low-resolution, near-infrared (NIR) spectra. Here, we present a detailed examination of the light-curve features in the optical data and an analysis of the NIR spectra. We place a lower limit on the spherical diameter of Chiron's nucleus of 160.2±1.3 km. Sharp, narrow dips were observed between 280-360 km from the centre (depending on event geometry). For a central chord and assumed ring plane, the separated features are 298.5-302 and 308-310.5 km from the nucleus, with normal optical depth ~0.5-0.9, and a gap of 9.1±1.3 km. These features are similar in equivalent depth to Chariklo's inner ring. The absence of absorbing/scattering material near the nucleus suggests that these sharp dips are more likely to be planar rings than a shell of material. The region of relatively-increased transmission is within the 1:2 spin-orbit resonance, consistent with the proposed clearing pattern for a non-axisymmetric nucleus. Characteristics of possible azimuthally incomplete features are presented, which could be transient, as well as a possible shell from ~900-1500 km: future observations are needed for confirmation. There are no significant features in the NIR light curves, nor any correlation between optical features and NIR spectral slope.