Nonthermal pickup ions (PUIs) are created in the solar wind (SW) by charge-exchange between SW ions (SWIs) and slow interstellar neutral atoms. It has long been theorized, but not directly observed that PUIs should be preferentially heated at quasiperpendicular shocks compared to thermal SWIs. We present in situ observations of interstellar hydrogen (H+) PUIs at an interplanetary shock by the New Horizons’ Solar Wind Around Pluto (SWAP) instrument at ~34 au from the Sun. At this shock, H+ PUIs are only a few percent of the total proton density but contain most of the internal particle pressure. A gradual reduction in SW flow speed and simultaneous heating of H+ SWIs is observed ahead of the shock, suggesting an upstream energetic particle pressure gradient. H+ SWIs lose ~85% of their energy flux across the shock and H+ PUIs are preferentially heated. Moreover, a PUI tail is observed downstream of the shock, such that the energy flux of all H+ PUIs is approximately six times that of H+ SWIs. We find that H+ PUIs, including their suprathermal tail, contain almost half of the total downstream energy flux in the shock frame.