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The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated for the first time by means of a direct numerical simulation. The freestream Mach number is equal to 9 and the oblique shock impinges with a cooled flat-plate boundary layer with an angle of 10°, generating a reversal flow region. In conjunction with freestream disturbances, the shock impingement triggers a transition to a fully turbulent regime shortly downstream of the interaction region. Accordingly, wall properties emphasize the presence of a laminar region, a recirculation bubble, a transitional zone and fully turbulent region. The breakdown to turbulence is characterized by an anomalous increase of skin friction and wall heat flux, due to the particular shock pattern. At the considered thermodynamic conditions the flow is found to be in a state of thermal non-equilibrium throughout, with non-equilibrium effects enhanced and sustained by the shock-induced laminar/turbulent transition, while chemical activity is almost negligible due to wall cooling. In the interaction region, relaxation towards thermal equilibrium is delayed and the fluctuating values of the rototranslational and the vibrational temperatures strongly differ, despite the strong wall-cooling. The fully turbulent portion exhibits evolutions of streamwise velocity, Reynolds stresses and turbulent Mach number in good accordance with previous results for highly-compressible cooled-wall boundary layers in thermal nonequilibrium, with turbulent motions sustaining thermal nonequilibrium. Nevertheless, the vibrational energy is found to contribute little to the total wall heat flux.