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The controllable incorporation of multiple immiscible elements into a single nanoparticle merits untold scientific and technological potential, yet remains a challenge using conventional synthetic techniques. We present a general route for alloying up to eight dissimilar elements into single-phase solid-solution nanoparticles, referred to as high-entropy-alloy nanoparticles (HEA-NPs), by thermally shocking precursor metal salt mixtures loaded onto carbon supports [temperature ~2000 kelvin (K), 55-millisecond duration, rate of ~105 K per second]. We synthesized a wide range of multicomponent nanoparticles with a desired chemistry (composition), size, and phase (solid solution, phase-separated) by controlling the carbothermal shock (CTS) parameters (substrate, temperature, shock duration, and heating/cooling rate). To prove utility, we synthesized quinary HEA-NPs as ammonia oxidation catalysts with ~100% conversion and >99% nitrogen oxide selectivity over prolonged operations.