We have cross matched the Gaia Data Release 1 secondary data set that contains positions of 1.14 billion objects against the most complete to date catalogue of very long baseline interferometry (VLBI) positions of 11.4 thousand sources, almost exclusively active galactic nuclei. We found 6064 matches, i.e. 53 per cent radio objects. The median uncertainty of VLBI positions is a factor of 4 smaller than the median uncertainties of their optical counterparts. Our analysis shows that the distribution of normalized arc lengths significantly deviates from Rayleigh shape with an excess of objects with small normalized arc lengths and with a number of outliers. We found that 6 per cent matches have radio-optical offsets significant at 99 per cent confidence level. Therefore, we conclude there exists a population of objects with genuine offsets between centroids of radio and optical emission.