  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 ($\sim3\times10^{10} M_{\odot}$), 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 $1.2\times10^{29}$ 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.
