The data release 1 (DR1) of milliarcsecond-scale accurate optical positions of stars and galaxies was recently published by the space mission Gaia. We study the offsets of highly accurate absolute radio (very long baseline interferometry, VLBI) and optical positions of active galactic nuclei (AGN) to see whether or not a signature of wavelength-dependent parsec-scale structure can be seen. We analyzed VLBI and Gaia positions and determined the direction of jets in 2957 AGNs from their VLBI images. We find that there is a statistically significant excess of sources with VLBI-to-Gaia position offset in directions along and opposite to the jet. Offsets along the jet vary from zero to tens of mas. Offsets in the opposite direction do not exceed 3 mas. The presense of strong, extended parsec-scale optical jet structures in many AGNs is required to explain all observed VLBI-Gaia offsets along the jet direction. The offsets in the opposite direction shorter than 1 mas can be explained either by a non-point-like VLBI jet structure or a core-shift effect due to synchrotron opacity.
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