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The formyl cation (HCO+) is one of the most abundant ions in molecular clouds and plays a major role in the interstellar chemistry. For this reason, accurate collisional rate coefficients for the rotational excitation of HCO+ and its isotopes due to the most abundant perturbing species in interstellar environments are crucial for non-local thermal equilibrium models and deserve special attention. In this work, we determined the first hyperfine resolved rate coefficients of HC17O+ in collision with H2 (j=0). Indeed, despite no scattering calculations on its collisional parameters have been performed so far, the HC17O+ isotope assumes a prominent role for astrophysical modelling applications. Computations are based on a new four dimensional (4D) potential energy surface, obtained at the CCSD(T)-F12a/aug-cc-pVQZ level of theory. A test on the corresponding cross section values pointed out that, to a good approximation, the influence of the coupling between rotational levels of H2 can be ignored. For this reason, the H2 collider has been treated as a spherical body and an average of the potential based on five orientations of H2 has been employed for scattering calculations. State-to-state rate coefficients resolved for the HC17O+ hyperfine structure for temperature ranging from 5 to 100 K have been computed using recoupling techniques. This study provides the first determination of HC17O+/H2 inelastic rate coefficients directly computed from full quantum close-coupling equations, thus supporting the reliability of future radiative transfer modellings of HC17O+ in interstellar environments.