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We present spatially resolved observations of Betelgeuse (Alpha Orionis) obtained with the Karl G. Jansky Very Large Array (VLA) at wavelengths of ~7mm (44~GHz) and ~1.3cm (22~GHz) on 2019 August 2, just prior to the onset of the historical optical dimming that occurred between late 2019 and early 2020. Our measurements suggest recent changes in the temperature and density structure of the atmosphere between radii r~2-3R*. At 7mm the star is ~20% dimmer than in previously published observing epochs between 1996--2004. We measure a mean gas temperature of T_B = 2270 +\- 260 K at r~2.1R*, where R* is the canonical photospheric radius. This is ~2 sigma lower than previously reported temperatures at comparable radii and >1200K lower than predicted by previous semi-empirical models of the atmosphere. The measured brightness temperature at r~2.6R* (T_B = 2580 +\- 260 K) is also cooler than expected based on trends in past measurements. The stellar brightness profile in our current measurements appears relatively smooth and symmetric, with no obvious signatures of giant convective cells or other surface features. However, the azimuthally averaged brightness profile is found to be more complex than a uniform elliptical disk. Our observations were obtained approximately six weeks before spectroscopic measurements in the ultraviolet revealed evidence of increases in the chromospheric electron density in the southern hemisphere of Betelgeuse, coupled with a large-scale outflow. We discuss possible scenarios linking these events with the observed radio properties of the star, including the passage of a strong shock wave.