The mechanical behavior of the single phase (fcc) CrMnFeCoNi high-entropy alloy (HEA) is examined in the dynamic regime. A series of experiments by dynamic-loading hat-shaped specimens using stopper rings to control the displacement are performed, and the alloy resists adiabatic shear-band formation up to a very large imposed shear strain of ∼7. It is proposed that the combination of the excellent strain-hardening ability and moderate thermal-softening effect retard shear localization. Recrystallized ultrafine-grained grains (diameters of 100–300 nm) with twins are revealed inside the shear band. Their formation is explained by the rotational dynamic recrystallization mechanism. The stability of the structure at high strain rates strongly suggests a high ballistic resistance for this class of alloys.