  In a Galactic core-collapse supernova (SN), axionlike particles (ALPs) could
be emitted via the Primakoff process and eventually convert into $\gamma$ rays
in the magnetic field of the Milky Way. From a data-driven sensitivity
estimate, we find that, for a SN exploding in our Galaxy, the Fermi Large Area
Telescope (LAT) would be able to explore the photon-ALP coupling down to
$g_{a\gamma} \simeq 2 \times 10^{-13}\,$GeV$^{-1}$ for an ALP mass $m_a
\lesssim 10^{-9}\,$eV. These values are out of reach of next generation
laboratory experiments. In this event, the Fermi LAT would probe large regions
of the ALP parameter space invoked to explain the anomalous transparency of the
Universe to $\gamma$ rays, stellar cooling anomalies, and cold dark matter. If
no $\gamma$-ray emission were to be detected, Fermi-LAT observations would
improve current bounds derived from SN1987A by more than one order of
magnitude.
