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Refractory high‐entropy alloys (RHEAs) show promising applications at high temperatures. However, achieving high strengths at elevated temperatures above 1173K is still challenging due to heat softening. Using intrinsic material characteristics as the alloy‐design principles, a single‐phase body‐centered‐cubic (BCC) CrMoNbV RHEA with high‐temperature strengths (beyond 1000 MPa at 1273 K) is designed, superior to other reported RHEAs as well as conventional superalloys. The origin of the high‐temperature strength is revealed by in situ neutron scattering, transmission‐electron microscopy, and first‐principles calculations. The CrMoNbV's elevated‐temperature strength retention up to 1273 K arises from its large atomic‐size and elastic‐modulus mismatches, the insensitive temperature dependence of elastic constants, and the dominance of non‐screw character dislocations caused by the strong solute pinning, which makes the solid‐solution strengthening pronounced. The alloy‐design principles and the insights in this study pave the way to design RHEAs with outstanding high‐temperature strength.