We report the detection of steady radio emission from the known X-ray source X9 in the globular cluster 47 Tuc. With a double-peaked C iv emission line in its ultraviolet spectrum providing a clear signature of accretion, this source had been previously classified as a cataclysmic variable. In deep ATCA (Australia Telescope Compact Array) imaging from 2010 and 2013, we identified a steady radio source at both 5.5 and 9.0 GHz, with a radio spectral index (defined as S ν ∝ να) of α = −0.4 ± 0.4. Our measured flux density of 42 ± 4 μJy beam−1 at 5.5 GHz implies a radio luminosity (νL ν) of 5.8 × 1027 erg s−1, significantly higher than any previous radio detection of an accreting white dwarf. Transitional millisecond pulsars, which have the highest radio-to-X-ray flux ratios among accreting neutron stars (still a factor of a few below accreting black holes at the same L X), show distinctly different patterns of X-ray and radio variability than X9. When combined with archival X-ray measurements, our radio detection places 47 Tuc X9 very close to the radio/X-ray correlation for accreting black holes, and we explore the possibility that this source is instead a quiescent stellar-mass black hole X-ray binary. The nature of the donor star is uncertain; although the luminosity of the optical counterpart is consistent with a low-mass main-sequence donor star, the mass transfer rate required to produce the high quiescent X-ray luminosity of 1033 erg s−1 suggests the system may instead be ultracompact, with an orbital period of order 25 min. This is the fourth quiescent black hole candidate discovered to date in a Galactic globular cluster, and the only one with a confirmed accretion signature from its optical/ultraviolet spectrum.