We present the first coordinated Very Long Baseline Array (VLBA) / Very Large Telescope Interferometer (VLTI) measurements of the stellar diameter and circumstellar atmosphere of a Mira variable star. Observations of the v = 1, J = 1-0 (43.1 GHz) and v = 2, J = 1-0 (42.8 GHz) SiO maser emission toward the Mira variable S Ori were conducted using the VLBA. Coordinated near-infrared K-band measurements of the stellar diameter were performed using VLTI-VINCI closely spaced in time to the VLBA observations. Analysis of the SiO maser data recorded at a visual variability phase 0.73 shows the average distance of the masers from the center of the distribution to be 9.4 mas for the v = 1 masers and 8.8 mas for the v = 2 masers. The velocity structure of the SiO masers appears to be random, with no significant indication of global expansion/infall or rotation. The determined near-infrared, K-band, uniform disk (UD) diameters decreased from similar to10.5 mas at phase 0.80 to similar to10.2 mas at phase 0.95. For the epoch of our VLBA measurements, an extrapolated UD diameter of Theta(UD)(K) = 10.8 +/- 0.3 mas was obtained, corresponding to a linear radius of R-UD(K) = 2.3 +/- 0.5 AU or R-UD(K) = 490 +/- 115 R.. Our coordinated VLBA/VLTI measurements show that the masers lie relatively close to the stellar photosphere at a distance of similar to2 photospheric radii, consistent with model estimates. This result is virtually free of the usual uncertainty inherent in comparing observations of variable stars widely separated in time and stellar phase.