  We report results from the first Earth-space VLBI observations of the
Galactic Center supermassive black hole, Sgr A*. These observations used the
space telescope Spektr-R of the RadioAstron project together with a global
network of 20 ground telescopes, observing at a wavelength of 1.35cm. Spektr-R
provided baselines up to 3.9 times the diameter of the Earth, corresponding to
an angular resolution of approximately 55 microarcseconds and a spatial
resolution of $5.5 R_{\rm Sch}$ at the source, where $R_{\rm Sch} \equiv 2 G
M/c^2$ is the Schwarzschild radius of Sgr A*. Our short ground baseline
measurements (<80 M\lambda) are consistent with an anisotropic Gaussian image,
while our intermediate ground baseline measurements (100-250 M\lambda) confirm
the presence of persistent image substructure in Sgr A*. Both features are
consistent with theoretical expectations for strong scattering in the ionized
interstellar medium, which produces Gaussian scatter-broadening on short
baselines and refractive substructure on long baselines. We do not detect
interferometric fringes on any of the longer ground baselines or on any
ground-space baselines. While space VLBI offers a promising pathway to sharper
angular resolution and the measurement of key gravitational signatures in black
holes, such as their photon rings, our results demonstrate that space VLBI
studies of Sgr A* will require sensitive observations at submillimeter
wavelengths.
