The half opening angle of a Kerr black-hole shadow is always equal to (5+-0.2)GM/Dc^2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of General Relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope. We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of +-4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A and the Earth, the effects of which will need to be corrected for in order for the black-hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ~9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this General Relativistic null hypothesis test with Event Horizon Telescope observations of Sgr A* to 10%.
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