  The preliminary detection of the Galactic Center black hole Sgr A* in X-rays
by the Chandra mission, as well as recent mm-VLBI measurements, impose strict
constraints on this source. Using a relativistic jet model for Sgr A*, we
calculate the synchrotron and synchrotron self-Compton emission. The predicted
spectrum provides an excellent fit to the radio spectrum and the the X-ray
observations. Limits on the infrared flux and the low X-ray flux require a
high-energy cut-off in the electron spectrum at gamma_e ~< 100. The implied
lack of a significant power-law tail of high-energy electrons also suppresses
the appearance of the extended, optically thin radio emission usually seen in
astrophysical jets. The jet therefore appears rather compact and naturally
satisfies current VLBI limits. The initial parameters of the model are tightly
constrained by the radio spectrum and the "submm-bump" in particular. While the
jet most likely is coupled to some kind of accretion flow, we suggest that the
most visible signatures can be produced by this outflow. If SSC emission from
the jet contributes to the Sgr A* spectrum, significant variability in X-rays
would be expected. The model could be generic for other low-luminosity AGN or
even X-ray binaries.
