The compact radio source Sgr A* is coincident with a 4 × 10⁶ M⊙ black hole at the dynamical center of the Galaxy and is surrounded by dense orbiting ionized and molecular gas. We present high-resolution radio continuum images of the central 3′ and report a faint continuous linear structure centered on Sgr A* with a P.A. 60°. The extension of this feature appears to be terminated symmetrically by two linearly polarized structures at 8.4GHz, 75″ from Sgr A*. A number of weak blobs of radio emission with X-ray counterparts are detected along the axis of the linear structure. The linear structure is best characterized by a mildly relativistic jet from Sgr A* with an outflow rate 10⁻⁶ M⊙yr⁻¹. The near and far sides of the jet are interacting with orbiting ionized and molecular gas over the last 1-3 hundred years and are responsible for a 2″ hole, the "minicavity," characterized by disturbed kinematics, enhanced Fe II/III line emission, and diffuse X-ray gas. The estimated kinetic luminosity of the outflow is ~1.2 × 10⁴¹erg s⁻¹, so the interaction with the bar may be responsible for the Galactic center X-ray flash inferred to be responsible for much of the fluorescent Fe Kα line emission from the inner 100pc of the Galaxy.