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We report the discovery of the repeating fast radio burst (FRB) source FRB 20240209A using the Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB telescope. We detected 22 bursts from this repeater between 2024 February and July, 6 of which were also recorded at the Outrigger station k’niʔatn k’l _⌣ stk’masqt (KKO). The multiple very long baseline interferometry localizations using the 66 km long CHIME–KKO baseline, each with a different baseline vector orientation due to the repeater’s high decl. of ∼86°, enabled the combined localization region to be constrained to 1″ × 2″. We present deep Gemini optical observations that, combined with the FRB localization, enabled a robust association of FRB 20240209A to the outskirts of a luminous galaxy (P(O∣x) = 0.99; L ≈ 5.3 × 10 ^10 L _⊙ ). FRB 20240209A has a projected physical offset of 40 ± 5 kpc from the center of its host galaxy, making it the FRB with the largest host galaxy offset to date. When normalized by the host galaxy size, the offset of FRB 20240209A (5.1 R _eff ) is comparable to that of FRB 20200120E (5.7 R _eff ), the only FRB source known to originate in a globular cluster. We consider several explanations for the large offset, including a progenitor that was kicked from the host galaxy or in situ formation in a low-luminosity satellite galaxy of the putative host, but find the most plausible scenario to be a globular cluster origin. This, coupled with the quiescent, elliptical nature of the host as demonstrated in our companion Letter, provides strong evidence for a delayed formation channel for the progenitor of the FRB source.