A 30-g xenon bubble chamber, operated at Northwestern University in June and November 2016, has for the first time observed simultaneous bubble nucleation and scintillation by nuclear recoils in a superheated liquid. This chamber is instrumented with a CCD camera for near-IR bubble imaging, a solar-blind photomultiplier tube to detect 175-nm xenon scintillation light, and a piezoelectric acoustic transducer to detect the ultrasonic emission from a growing bubble. The time of nucleation determined from the acoustic signal is used to correlate specific scintillation pulses with bubble-nucleating events. We report on data from this chamber for thermodynamic "Seitz" thresholds from 4.2 to 15.0 keV. The observed single- and multiple-bubble rates when exposed to a ^{252}Cf neutron source indicate that, for an 8.3-keV thermodynamic threshold, the minimum nuclear recoil energy required to nucleate a bubble is 19±6 keV (1σ uncertainty). This is consistent with the observed scintillation spectrum for bubble-nucleating events. We see no evidence for bubble nucleation by gamma rays at any of the thresholds studied, setting a 90% C.L. upper limit of 6.3×10^{-7} bubbles per gamma interaction at a 4.2-keV thermodynamic threshold. This indicates stronger gamma discrimination than in CF_{3}I bubble chambers, supporting the hypothesis that scintillation production suppresses bubble nucleation by electron recoils, while nuclear recoils nucleate bubbles as usual. These measurements establish the noble-liquid bubble chamber as a promising new technology for the detection of weakly interacting massive particle dark matter and coherent elastic neutrino-nucleus scattering.