  We present evidence of tidally-driven inspiral in the Kepler-1658 (KOI-4)
system, which consists of a giant planet (1.1$R_\mathrm{J}$, 5.9$M_\mathrm{J}$)
orbiting an evolved host star (2.9$R_\odot$, 1.5$M_\odot$). Using transit
timing measurements from Kepler, Palomar/WIRC, and TESS, we show that the
orbital period of Kepler-1658b appears to be decreasing at a rate $\dot{P} =
131_{-22}^{+20}$~ms~yr$^{-1}$, corresponding to an infall timescale
$P/\dot{P}\approx2.5$~Myr. We consider other explanations for the data
including line-of-sight acceleration and orbital precession, but find them to
be implausible. The observed period derivative implies a tidal quality factor
$Q_\star' = 2.50_{-0.62}^{+0.85}\times10^4$, in good agreement with theoretical
predictions for inertial wave dissipation in subgiant stars. Additionally,
while it probably cannot explain the entire inspiral rate, a small amount of
planetary dissipation could naturally explain the deep optical eclipse observed
for the planet via enhanced thermal emission. As the first evolved system with
detected inspiral, Kepler-1658 is a new benchmark for understanding tidal
physics at the end of the planetary life cycle.
