The recent detection of polarized radiation from Sgr A* requires a non-thermal electron distribution for the emitting plasma. The Faraday rotation measure must be small, placing strong limits on the density and magnetic field strength. We show that these constraints rule out advection-dominated accretion flow models. We construct a simple two-component model which can reproduce both the radio to mm spectrum and the polarization. This model predicts that the polarization should rise to nearly 100% at shorter wavelengths. The first component, possibly a black-hole powered jet, is compact, low density, and self-absorbed near 1 mm with ordered magnetic field, relativistic Alfvén speed, and a non-thermal electron distribution. The second component is poorly constrained, but may be a convection-dominated accretion flow with \dot M 10-9Mo/yr, in which feedback from accretion onto the black hole suppresses the accretion rate at large radii. The black hole shadow should be detectable with sub-mm VLBI.