  The well-studied M9 dwarf TVLM 513-46546 is a rapid rotator (P_rot ~ 2 hr)
hosting a stable, dipolar magnetic field of ~3 kG surface strength. Here we
report its detection with ALMA at 95 GHz at a mean flux density of $56 \pm 12$
uJy, making it the first ultracool dwarf detected in the millimeter band,
excluding young, disk-bearing objects. We also report flux density measurements
from unpublished archival VLA data and new optical monitoring data from the
Liverpool Telescope. The ALMA data are consistent with a power-law radio
spectrum that extends continuously between centimeter and millimeter
wavelengths. We argue that the emission is due to the synchrotron process,
excluding thermal, free-free, and electron cyclotron maser emission as possible
sources. During the interval of the ALMA observation that phases with the
maximum of the object's optical variability, the flux density is higher at a
~1.8 sigma significance level. These early results show how ALMA opens a new
window for studying the magnetic activity of ultracool dwarfs, particularly
shedding light on the particle acceleration mechanism operating in their
immediate surroundings.
