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Abstract The discovery and localization of FRB 20240209A by the Canadian Hydrogen Intensity Mapping Fast Radio Burst (CHIME/FRB) experiment marks the first repeating FRB localized with the CHIME/FRB Outriggers and adds to the small sample of repeating FRBs with associated host galaxies. Here we present Keck and Gemini observations of the host that reveal a redshiftz = 0.1384 ± 0.0004. We perform stellar population modeling to jointly fit the optical through mid-IR data of the host and infer a median stellar mass log(M_*/M_⊙) = 11.35 ± 0.01 and a mass-weighted stellar population age  ~11 Gyr, corresponding to the most massive and oldest FRB host discovered to date. Coupled with a star formation rate  <0.31M_⊙yr⁻¹, the specific star formation rate  <10^−11.9yr⁻¹classifies the host as quiescent. Through surface brightness profile modeling, we determine an elliptical galaxy morphology, marking the host as the first confirmed elliptical FRB host. The discovery of a quiescent early-type host galaxy within a transient class predominantly characterized by late-type star-forming hosts is reminiscent of short-duration gamma-ray bursts, Type Ia supernovae, and ultraluminous X-ray sources. Based on these shared host demographics, coupled with a large offset as demonstrated in our companion Letter, we conclude that preferred sources for FRB 20240209A include magnetars formed through merging binary neutron stars/white dwarfs or the accretion-induced collapse of a white dwarf, or a luminous X-ray binary. Together with FRB 20200120E localized to a globular cluster in M81, our findings provide strong evidence that some fraction of FRBs may arise from a process distinct from the core collapse of massive stars.