Fast radio bursts (FRBs) are millisecond-duration pulses of radio emission originating from extragalactic distances. Radio dispersion is imparted on each burst by intervening plasma, mostly located in the intergalactic medium. In this work, we observe the burst FRB 20220610A and localize it to a morphologically complex host galaxy system at redshift 1.016 ± 0.002. The burst redshift and dispersion measure are consistent with passage through a substantial column of plasma in the intergalactic medium and extend the relationship between those quantities measured at lower redshift. The burst shows evidence for passage through additional turbulent magnetized plasma, potentially associated with the host galaxy. We use the burst energy of 2 × 10 42 erg to revise the empirical maximum energy of an FRB. Editor’s summary Fast radio bursts (FRBs) are brief flashes of radio emission from extragalactic sources. Ryder et al . detected a FRB and localized its source to a galaxy at a redshift of about 1, more than halfway back to the Big Bang. The burst is unusually bright, challenging models of the FRB emission mechanism. The authors also investigated how the intergalactic medium causes dispersion of the radio waves, finding more dispersion than expected from a correlation measured at lower redshift. They inferred the presence of magnetized plasma within the host galaxy, which has a complex morphology. —Keith T. Smith A fast radio burst is localized to a distant galaxy, indicating that its intrinsic brightness is unusually high.