  We report the first search for the $K_L \to \pi^0 \gamma$ decay, which is
forbidden by Lorentz invariance, using the data from 2016 to 2018 at the J-PARC
KOTO experiment. With a single event sensitivity of $(7.1\pm 0.3_{\rm stat.}
\pm 1.6_{\rm syst.})\times 10^{-8}$, no candidate event was observed in the
signal region. The upper limit on the branching fraction was set to be
$1.7\times 10^{-7}$ at the 90\% confidence level.
