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CrCoNi exhibits the best combination of strength and ductility among all the equiatomic single-phase FCC subsets of the CrMnFeCoNi high-entropy alloy. Here, its yield strength was determined in compression as a function of grain size and temperature. Yield strength was also plotted as a function of “crystallite” size, which takes into account both annealing twin boundaries and grain boundaries. The resulting Hall-Petch slopes were straight lines but with different slopes that depend on the number of twin boundaries per grain. Scanning transmission electron microscopy of deformed specimens revealed the formation of dislocation pile-ups at grain and annealing twin boundaries indicating that the latter also act as obstacles to slip and contribute to strength. Using a simple pile-up model, the strengths of the grain and twin boundaries were estimated to lie in the range 900–1250 MPa. Assuming that they have the same strength, in the case of twin boundaries this strength corresponds roughly to the stress required to constrict Shockley partials, which suggests that dissociated dislocations have to become compact before they can cross the annealing twin boundaries.