We revise the bound from the supernova SN1987A on the coupling of ultralight axion-like particles (ALPs) to photons. In a core-collapse supernova, ALPs would be emitted via the Primakoff process, and eventually convert into gamma rays in the magnetic field of the Milky Way. The lack of a gamma-ray signal in the GRS instrument of the SMM satellite in coincidence with the observation of the neutrinos emitted from SN1987A therefore provides a strong bound on their coupling to photons. Due to the large uncertainty associated with the current bound, we revise this argument, based on state-of-the-art physical inputs both for the supernova models and for the Milky-Way magnetic field. Furthermore, we provide major amendments, such as the consistent treatment of nucleon-degeneracy effects and of the reduction of the nuclear masses in the hot and dense nuclear medium of the supernova. With these improvements, we obtain a new upper limit on the photon-ALP coupling: g(a gamma) less than or similar to 5.3 x 10(-12) GeV-1, for m(a) less than or similar to 4.4 x 10(-10) eV, and we also give its dependence at larger ALP masses m(a). Moreover, we discuss how much the Fermi-LAT satellite experiment could improve this bound, should a close-enough supernova explode in the near future.