Among the most powerful techniques for the exploration of the Universe is very long baseline interferometry (VLBI), which is based on the simultaneous observation of radio sources in the sky with arrays of distant ground-based antennas. One of the effects currently limiting its ultimate sensitivity is the phase-instability of the reference clocks adopted at each antenna. This term can be made negligible delivering the same clock signal to multiple telescope sites using optical fibers. We realized such an infrastructure by disseminating a coherent optical frequency signal to two distant radio telescopes using a 1739-km-long fiber. We performed a 24 h geodetic VLBI campaign in which the same clock reference was used at both telescopes and analyzed it using standard VLBI procedures. The results were consistent with the expectations, confirming that the proposed approach is feasible and configures as a novel tool for studying the role of clocks, troposphere, and systematic effects in the ultimate VLBI resolution.