Axion-like particles (ALPs) can induce localized oscillatory modulations in the spectra of photon sources passing through astrophysical magnetic fields. Ultra-deep Chandra observations of the Perseus cluster contain over 5×105 counts from the active galactic nucleus (AGN) of the central cluster galaxy NGC1275 and represent a data set of extraordinary quality for ALP searches. We use this data set to search for X-ray spectral irregularities from the AGN. The absence of irregularities at the O(30%) level allows us to place leading constraints on the ALP-photon mixing parameter {g}_{a\gamma \gamma }\lesssim 1.4\mbox{--}4.0\times {10}^{-12}\,{\mathrm{GeV}}^{-1} for ma≲10−12eV, depending on assumptions on the magnetic field realization along the line of sight.European Research Counci