Centaurus A (Cen A) is a bright radio source associated with the nearby galaxy NGC 5128 where high-resolution radio observations can probe the jet at scales of less than a light day. The South Pole Telescope (SPT) and the Atacama Pathfinder Experiment performed a single-baseline very-long-baseline interferometry (VLBI) observation of Cen A in 2015 January as part of VLBI receiver deployment for the SPT. We measure the correlated flux density of Cen A at a wavelength of 1.4 mm on a similar to 7000 km (5 G lambda) baseline. Ascribing this correlated flux density to the core, and with the use of a contemporaneous short-baseline flux density from a Submillimeter Array observation, we infer a core brightness temperature of 1.4 x 10(11) K. This is close to the equipartition brightness temperature, where the magnetic and relativistic particle energy densities are equal. Under the assumption of a circular Gaussian core component, we derive an upper limit to the core size phi = 34.0 +/- 1.8 mu as, corresponding to 120 Schwarzschild radii for a black hole mass of 5.5 x. 10(7) M-circle dot.