Axion-Like Particles (ALPs) are predicted by several Beyond the Standard Model theories, in particular, string theory. In the presence of an external magnetic field perpendicular to the direction of propagation, ALPs can couple to photons. Therefore, if an X-ray source is viewed through a magnetised plasma, such as a luminous quasar in a galaxy cluster, we may expect spectral distortions that are well described by photon-ALP oscillations. We present a $571 mathrm{ks}$ combined High and Low Energy Transmission Grating (HETG/LETG) Chandra observation of the powerful radio-quiet quasar H1821+643, hosted by a cool-core cluster at redshift $0.3$. The spectrum is well described by a double power-law continuum and broad$+$narrow iron line emission typical of type-1 Active Galactic Nuclei (AGN), with remaining spectral features $< 2.5%$. Using a cell-based approach to describe the turbulent cluster magnetic field, we compare our spectrum with photon-ALP mixing curves for 500 field realisations assuming that the thermal-to-magnetic pressure ratio remains constant up to the virial radius. At $99.7%$ credibility, we exclude all couplings $g_mathrm{agamma} > 6.3 times 10^{-13} {mathrm{GeV}}^{-1}$ for most ALP masses $< 10^{-12} mathrm{eV}$. Our results are moderately more sensitive to constraining ALPs than the best previous result from Chandra observations of the Perseus cluster, albeit with a less constrained field model. We provide the best constraints on light ALPs, exceeding the projected sensitivity of next generation axion helioscopes. We reflect on the promising future of ALP studies with bright AGN embedded in rich clusters, especially with the upcoming Athena mission.
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