A black hole can launch a powerful relativistic jet after it tidally disrupts a star. If this jet fortuitously aligns with our line of sight, the overall brightness is Doppler boosted by several orders of magnitude. Consequently, such on-axis relativistic tidal disruption events have the potential to unveil cosmological (redshift z > 1) quiescent black holes and are ideal test beds for understanding the radiative mechanisms operating in super-Eddington jets. Here we present multiwavelength (X-ray, UV, optical and radio) observations of the optically discovered transient AT 2022cmc at z = 1.193. Its unusual X-ray properties, including a peak observed luminosity of ≳10⁴⁸ erg s−1, systematic variability on timescales as short as 1,000 s and overall duration lasting more than 30 days in the rest frame, are traits associated with relativistic tidal disruption events. The X-ray to radio spectral energy distributions spanning 5–50 days after discovery can be explained as synchrotron emission from a relativistic jet (radio), synchrotron self-Compton (X-rays) and thermal emission similar to that seen in low-redshift tidal disruption events (UV/optical). Our modelling implies a beamed, highly relativistic jet akin to blazars but requires extreme matter domination (that is, a high ratio of electron-to-magnetic-field energy densities in the jet) and challenges our theoretical understanding of jets.