  {\it Chandra} spectroscopy of transient stellar-mass black holes in outburst
has clearly revealed accretion disk winds in soft, disk--dominated states, in
apparent anti-correlation with relativistic jets in low/hard states. These disk
winds are observed to be highly ionized, dense, and to have typical velocities
of $\sim$1000 km/s or less projected along our line of sight. Here, we present
an analysis of two {\it Chandra} High Energy Transmission Grating spectra of
the Galactic black hole candidate IGR J17091$-$3624 and contemporaneous EVLA
radio observations, obtained in 2011. The second {\it Chandra} observation
reveals an absorption line at 6.91$\pm$0.01 keV; associating this line with
He-like Fe XXV requires a blue-shift of $9300^{+500}_{-400}$ km/s (0.03$c$, or
the escape velocity at 1000 R$_{Schw}$). This projected outflow velocity is an
order of magnitude higher than has previously been observed in stellar-mass
black holes, and is broadly consistent with some of the fastest winds detected
in active galactic nuclei. A potential feature at 7.32 keV, if due to Fe XXVI,
would imply a velocity of $\sim 14600$ km/s (0.05$c$), but this putative
feature is marginal. Photoionization modeling suggests that the accretion disk
wind in IGR J17091$-$3624 may originate within 43,300 Schwarzschild radii of
the black hole, and may be expelling more gas than accretes. The
contemporaneous EVLA observations strongly indicate that jet activity was
indeed quenched at the time of our {\it Chandra} observations. We discuss the
results in the context of disk winds, jets, and basic accretion disk physics in
accreting black hole systems.
