We introduce a setup to measure high-resolution inelastic x-ray scattering at the High Energy Density scientific instrument at the European X-Ray Free-Electron Laser (XFEL). The setup uses the Si (533) reflection in a channel-cut monochromator and three spherical diced analyzer crystals in near-backscattering geometry to reach a high spectral resolution. An energy resolution of 44 meV is demonstrated for the experimental setup, close to the theoretically achievable minimum resolution. The analyzer crystals and detector are mounted on a curved-rail system, allowing quick and reliable changes in scattering angle without breaking vacuum. The entire setup is designed for operation at 10 Hz, the same repetition rate as the high-power lasers available at the instrument and the fundamental repetition rate of the European XFEL. Among other measurements, it is envisioned that this setup will allow studies of the dynamics of highly transient laser generated states of matter.