A list of 205 gamma-ray strong objects was reported recently as a result of a 3-month integration with the Large Area Telescope on board the Fermi Gamma-Ray Space Telescope. We attempted identification of these objects, cross-correlating the gamma-ray positions with VLBI positions of a large all-sky sample of extragalactic radio sources selected on the basis of their parsec-scale flux density. The original associations reported by the Fermi team are confirmed and six new identifications are suggested. A Monte-Carlo analysis shows that the fraction of chance associations in our analysis is less than 5 per cent, and confirms that the vast majority of gamma-ray bright extragalactic sources are radio loud blazars with strong parsec-scale jets. A correlation between the parsec-scale radio and gamma-ray flux is supported by our analysis of a complete VLBI flux-density-limited sample of extragalactic jets. The effectiveness of using a VLBI catalog to find associations between gamma-ray detections and compact extragalactic radio sources, especially near the Galactic plane, is demonstrated. It is suggested that VLBI catalogs should be used for future identification of Fermi LAT objects.