Deformation twinning was investigated in single-phase face-centered-cubic (FCC) high-entropy alloys of the CrxMn20Fe20Co20Ni40-x system (14 ≤ x ≤ 26 at.%). The intrinsic stacking fault energies (γisf) of these alloys varied systematically across this composition range, but other physical properties that have the potential of affecting deformation twinning remained constant allowing us to isolate the effects of γisf on twinning. Tensile tests were performed at 293 and 77 K, and the tests interrupted at several different strains to evaluate deformation-induced changes in microstructure by transmission electron microscopy. The critical stress above which deformation twinning occurs was thus determined. We also evaluated how grain size (19 ≤ d ≤ 237 µm) affects the yield stress (σy) and the uniaxial critical twinning stress (σtw), which allowed us to subtract the corresponding Hall-Petch contributions and compare our polycrystalline results with experimental and theoretical data reported for single crystals. Taking into account the critical resolved shear stresses for deformation twinning in our alloys (τtw) along with those of FCC pure metals and binary alloys reported in the literature, we derived the following relationship that rationalizes most of the experimental data: τtw = 10-3G + γisf/(3·bp), where G is the shear modulus and bp is the magnitude of the Burgers vector of a Shockley partial dislocation. This expression, involving only measurable material properties, can serve as a basis for the design and optimization of new HEAs with tunable twinning stresses and, in turn, exceptional strength-ductility combinations.