  We present the discovery and characterization of a radio-bright binary in the
Galactic globular cluster M10. First identified in deep radio continuum data
from the Karl G. Jansky Very Large Array, M10-VLA1 has a flux density of
$27\pm4$ $\mu$Jy at 7.4 GHz and a flat to inverted radio spectrum. Chandra
imaging shows an X-ray source with $L_X \approx 10^{31}$ erg s$^{-1}$ matching
the location of the radio source. This places M10-VLA1 within the scatter of
the radio--X-ray luminosity correlation for quiescent stellar-mass black holes,
and a black hole X-ray binary is a viable explanation for this system. The
radio and X-ray properties of the source disfavor, though do not rule out,
identification as an accreting neutron star or white dwarf system. Optical
imaging from the Hubble Space Telescope and spectroscopy from the SOAR
telescope show the system has an orbital period of 3.339 d and an unusual "red
straggler" component: an evolved star found redward of M10's red giant branch.
These data also show UV/optical variability and double-peaked H$\alpha$
emission characteristic of an accretion disk. However, SOAR spectroscopic
monitoring reveals that the velocity semi-amplitude of the red straggler is
low. We conclude that M10-VLA1 is most likely either a quiescent black hole
X-ray binary with a rather face-on ($ i < $ 4$^{\circ}$) orientation or an
unusual flaring RS CVn-type active binary, and discuss future observations that
could distinguish between these possibilities.
