The physical properties of fast radio burst (FRB) host galaxies provide important clues towards the nature of FRB sources. The 16 FRB hosts identified thus far span three orders of magnitude in mass and specific star-formation rate, implicating a ubiquitously occurring progenitor object. FRBs localised with ~arcsecond accuracy also enable effective searches for associated multi-wavelength and multi-timescale counterparts, such as the persistent radio source associated with FRB 20121102A. Here we present a localisation of the repeating source FRB 20201124A, and its association with a host galaxy (SDSS J050803.48+260338.0, z=0.098) and persistent radio source. The galaxy is massive ($sim3times10^{10} M_{odot}$), star-forming (few solar masses per year), and dusty. Very Large Array and Very Long Baseline Array observations of the persistent radio source measure a luminosity of $1.2times10^{29}$ erg s$^{-1}$ Hz$^{-1}$, and show that is extended on scales $gtrsim50$ mas. We associate this radio emission with the ongoing star-formation activity in SDSS J050803.48+260338.0. Deeper, more detailed observations are required to better utilise the milliarcsecond-scale localisation of FRB 20201124A reported from the European VLBI Network, and determine the origin of the large dispersion measure ($150-220$ pc cm$^{-3}$) contributed by the host. SDSS J050803.48+260338.0 is an order of magnitude more massive than any galaxy or stellar system previously associated with a repeating FRB source, but is comparable to the hosts of so far non-repeating FRBs, further building the link between the two apparent populations.
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