AbstractThe dispersive sweep of fast radio bursts (FRBs) has been used to probe the ionized baryon content of the intergalactic medium¹, which is assumed to dominate the total extragalactic dispersion. Although the host-galaxy contributions to the dispersion measure appear to be small for most FRBs², in at least one case there is evidence for an extreme magneto-ionic local environment^3,4 and a compact persistent radio source⁵. Here we report the detection and localization of the repeating FRB 20190520B, which is co-located with a compact, persistent radio source and associated with a dwarf host galaxy of high specific-star-formation rate at a redshift of 0.241 ± 0.001. The estimated host-galaxy dispersion measure of approximately ${903}_{-111}^{+72}$ 903 − 111 + 72 parsecs per cubic centimetre, which is nearly an order of magnitude higher than the average of FRB host galaxies^2,6, far exceeds the dispersion-measure contribution of the intergalactic medium. Caution is thus warranted in inferring redshifts for FRBs without accurate host-galaxy identifications.