We report the detection of the two-dimensional structure of the radio source associated with the Galactic Center black hole, Sagittarius A*, obtained from Very Long Baseline Array observations at a wavelength of 7 mm. The intrinsic source is modeled as an elliptical Gaussian with major-axis size 35.4 × 12.6 RS in position angle 95° east of north. This morphology can be interpreted in the context of both jet and accretion disk models for the radio emission. There is supporting evidence in large angular-scale multi-wavelength observations for both source models for a preferred axis near 95°. We also place a maximum peak-to-peak change of 15% in the intrinsic major-axis size over five different epochs. Three observations were triggered by detection of near infrared (NIR) flares and one was simultaneous with a large X-ray flare detected by NuSTAR. The absence of simultaneous and quasi-simultaneous flares indicates that not all high energy events produce variability at radio wavelengths. This supports the conclusion that NIR and X-ray flares are primarily due to electron excitation and not to an enhanced accretion rate onto the black hole. © 2014. The American Astronomical Society. All rights reserved..