CORE-DOMINATED radio sources associated with quasars are a manifestation of the most extreme form of activity in galactic nuclei. In general, the morphology of their inner radio structure is in the form of a jet detected on only one side of the core; the larger-scale radio emission is relatively symmetric1. Superluminal motion in some sources2,3 has led to the suggestion that the ejection of radio-emitting material is relativistic and intrinsically two-sided. The apparent one-sidedness of the jets is then explained by relativistic aberration4-6. This persuasive interpretation has not escaped criticism: both physical7 and statistical8 arguments have been advanced in favour of one-sided ejection. However, our new optical observations of 3C120, which reveal the details of the interaction between the radio jet and the quiescent gas in the galaxy, offer significant kinematic evidence in favour of the relativistic-beaming hypothesis.