Most known planets are found around metal-rich host stars, which has made it difficult to determine whether a lower metallicity limit for planet formation exists and how the properties of planets born in low-metallicity environments may differ from those with metal-rich origins. We present the discovery and characterization of TOI-7169 b (TIC 372048733 b), a hot Jupiter that is orbiting a spectroscopically confirmed metal-poor ([Fe/H] = −0.72 ± 0.05) host star. Based on photometry from TESS and follow-up ground-based imaging, we measure an orbital period of 3.4373125−0.0000019+0.0000020 days and a planetary radius of 1.475 ± 0.029 RJup. We use TRES spectroscopy to determine a mass for TOI-7169 b of 0.41 ± 0.14 MJup. The planet is therefore inflated, with a low density of 0.159−0.054+0.055 g cm−3. We also characterize the host star, showing that TOI-7169 is ancient (12.3 ± 0.6 Gyr) and α enhanced ([α/Fe] ≍ 0.3), but with a Galactocentric orbit that is confined to the thin disk. TOI-7169 is perhaps the oldest and most metal-poor star currently known to host a transiting giant planet. Future transmission spectroscopy probing the atmosphere of TOI-7169 b may provide insight into the effect of metallicity on the physical properties of giant planets.