Context: The highest redshift quasars at z>~6 receive considerable attention since they provide strong constraints on the growth of the earliest supermassive black holes. They also probe the epoch of reionisation and serve as "lighthouses" to illuminate the space between them and the observer. The source J1427+3312 (z=6.12) has recently been identified as the first and so far the only known radio-loud quasar at z>6. Aims: We investigated the compact radio structure of J1427+3312 on

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... nd (mas) angular scales, to compare it with that of the second most distant radio-loud quasar J0836+0054 (z=5.77) and with lower-redshift radio quasars in general. Methods: We observed J1427+3312 in phase-reference mode with ten antennas of the European Very Long Baseline Interferometry (VLBI) Network (EVN) at 1.6 GHz on 11 March 2007 and at 5 GHz on 3 March 2007. Results: The source was clearly detected at both frequencies. At 1.6 GHz, it shows a prominent double structure. The two components are separated by 8.3 mas, corresponding to a projected linear distance of ~160 pc. Both components with sub-mJy flux densities appear resolved. In the position of the brightest component at 1.6 GHz, we detected mas-scale radio emission at 5 GHz as well. The radio spectrum of this feature is steep. The double structure and the separation of the components of J1427+3312 are similar to those of the young (<~10^4 yr) compact symmetric objects (CSOs).