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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 × 10⁴² erg to revise the empirical maximum energy of an FRB.