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We report about a 230 GHz very long baseline interferometry (VLBI) fringe finder observation of blazar 3C 279 with the APEX telescope in Chile, the phased submillimeter array (SMA), and the SMT of the Arizona Radio Observatory (ARO). We installed VLBI equipment and measured the APEX station position to 1 cm accuracy (1 sigma). We then observed 3C 279 on 2012 May 7 in a 5 hour 230 GHz VLBI track with baseline lengths of 2800 M$\lambda$ to 7200 M$\lambda$ and a finest fringe spacing of 28.6 micro-arcseconds. Fringes were detected on all baselines with SNRs of 12 to 55 in 420 s. The correlated flux density on the longest baseline was ~0.3 Jy/beam, out of a total flux density of 19.8 Jy. Visibility data suggest an emission region <38 uas in size, and at least two components, possibly polarized. We find a lower limit of the brightness temperature of the inner jet region of about 10^10 K. Lastly, we find an upper limit of 20% on the linear polarization fraction at a fringe spacing of ~38 uas. With APEX the angular resolution of 230 GHz VLBI improves to 28.6 uas. This allows one to resolve the last-photon ring around the Galactic Center black hole event horizon, expected to be 40 uas in diameter, and probe radio jet launching at unprecedented resolution, down to a few gravitational radii in galaxies like M 87. To probe the structure in the inner parsecs of 3C 279 in detail, follow-up observations with APEX and five other mm-VLBI stations have been conducted (March 2013) and are being analyzed.