Axion-like particles (ALPs) can induce localised oscillatory modulations in the spectra of photon sources passing through astrophysical magnetic fields. Ultra-deep Chandra observations of the Perseus cluster contain over $5 \times 10^5$ counts from the AGN of the central cluster galaxy NGC1275, and represent a dataset of extraordinary quality for ALP searches. We use this dataset 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 $g_{a\gamma\gamma} \lesssim 1.4 - 4.0 \times 10^{-12} {\rm GeV}^{-1}m_a \lesssim 10^{-12}$ eV, depending on assumptions on the magnetic field realisation along the line of sight.

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