Kepler1627A is a G8V star previously known to host a 3.8R{Earth} planet on a 7.2day orbit. The star was observed by the Kepler space telescope because it is nearby (d=329pc) and it resembles the Sun. Here, we show using Gaia kinematics, TESS stellar rotation periods, and spectroscopic lithium abundances that Kepler1627 is a member of the 38_-5_^+6^Myr old {delta}Lyr cluster. To our knowledge, this makes Kepler1627Ab the youngest planet with a precise age yet found by the prime Kepler mission. The Kepler photometry shows two peculiarities: the average transit profile is asymmetric, and the individual transit times might be correlated with the local light- curve slope. We discuss possible explanations for each anomaly. More importantly, the {delta}Lyr cluster is one of ~103 coeval groups whose properties have been clarified by Gaia. Many other exoplanet hosts are candidate members of these clusters; their ages can be verified with the trifecta of Gaia, TESS, and ground-based spectroscopy.