Supermassive black holes at the centre of active galactic nuclei power some of the most luminous objects in the Universe. Typically, very long baseline interferometric (VLBI) observations of blazars have revealed only funnel-like morphologies with little information of the ejected plasma internal structure. Here we show extremely-high angular resolution images of the blazar 3C279 obtained with the space VLBI mission RadioAstron, which allowed us to resolve the jet transversely and reveal several filaments produced by Kelvin–Helmholtz instabilities in a kinetically dominated flow that originate from the VLBI core and extend up to 175 parsecs (de-projected) downstream the jet. The VLBI core appears to be elongated, in agreement with recent Event Horizon Telescope results, but thanks to our higher dynamic range and increased field of view we are able to connect the immediate environment of the supermassive black hole with the large-scale jet. From the observed linear polarization and strong cross-section emission asymmetry we can infer that the filaments are threaded by a helical magnetic field rotating clockwise, as seen in the direction of the flow motion, with an intrinsic helix pitch angle of ~45 degrees in a jet with a Lorentz factor of ~13.