{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.
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