  Kepler 1627A is a G8V star previously known to host a 3.8 Earth-radius planet
on a 7.2 day orbit. The star was observed by the Kepler space telescope because
it is nearby (d=329 pc) and it resembles the Sun. Here we show using Gaia
kinematics, TESS stellar rotation periods, and spectroscopic lithium abundances
that Kepler 1627 is a member of the 38 $\pm$ 6 Myr old $\delta$ Lyr cluster. To
our knowledge, this makes Kepler 1627Ab 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 about 10$^3$ coeval groups whose properties have been
clarified by Gaia. Many other exoplanet hosts are candidate members of these
clusters; these memberships can be verified with the trifecta of Gaia, TESS,
and ground-based spectroscopy.
