ABSTRACT: By means of near-simultaneous multi-wavelength VLBA measurements, we determine for the first time the intrinsic size of Sgr A ^\star to be 72 R_sc(\star) by < 20 R_sc(\star), with the major axis oriented essentially north-south, where R_sc(\star) \equiv 7.5 * 1011 cm is the Schwarzschild radius for a 2.5*106 Mo black hole. Contrary to previous expectation that the intrinsic structure of Sgr A ^\star is observable only at lambda <= 1 mm, we can discern the intrinsic source size at lambda 7 mm because (1) the scattering size along the minor axis is half that along the major axis, and (2) the near simultaneous multi-wavelength mapping of Sgr A^\star makes it possible to extrapolate precisely the minor axis scattering angle at lambda 7 mm. The intrinsic size and shape place direct constraints on the various emission models for Sgr A ^\star. In particular, the advection dominated accretion flow model may have to incorporate a radio jet in order to account for the structure of Sgr A ^\star.