47 Tuc X9 is a low-mass X-ray binary (LMXB) in the globular cluster 47 Tucanae, and was previously thought to be a cataclysmic variable. However, Miller-Jones et al. recently identified a radio counterpart to X9 (inferring a radio X-ray luminosity ratio consistent with black hole LMXBs), and suggested that the donor star might be a white dwarf. We report simultaneous observations of X9 performed by Chandra, NuSTAR and Australia Telescope Compact Array. We find a clear 28.18+/- 0.02-min periodic modulation in the Chandra data, which we identify as the orbital period, confirming this system as an ultracompact X-ray binary. Our X-ray spectral fitting provides evidence for photoionized gas having a high oxygen abundance in this system, which indicates a CO white dwarf donor. We also identify reflection features in the hard X-ray spectrum, making X9 the faintest LMXB to show X-ray reflection. We detect an approx. 6.8-d modulation in the X-ray brightness by a factor of 10, in archival Chandra, Swift and ROSAT data. The simultaneous radio X-ray flux ratio is consistent with either a black hole primary or a neutron star primary, if the neutron star is a transitional millisecond pulsar. Considering the measured orbital period (with other evidence of a white dwarf donor), and the lack of transitional millisecond pulsar features in the X-ray light curve, we suggest that this could be the first ultracompact black hole X-ray binary identified in our Galaxy.