High-entropy alloys (HEAs) comprise a novel class of scientifically and technologically interesting materials. Among these, equatomic CrMnFeCoNi with the face-centered cubic (FCC) structure is noteworthy because its ductility and strength increase with decreasing temperature while maintaining outstanding fracture toughness at cryogenic temperatures. Here we report for the first time by single-crystal micropillar compression that its bulk room temperature critical resolved shear stress (CRSS) is ~33–43 MPa, ~10 times higher than that of pure nickel. CRSS depends on pillar size with an inverse power-law scaling exponent of –0.63 independent of orientation. Planar ½ < 110 > {111} dislocations dissociate into Shockley partials whose separations range from ~3.5–4.5 nm near the screw orientation to ~5–8 nm near the edge, yielding a stacking fault energy of 30 ± 5 mJ/m2. Dislocations are smoothly curved without any preferred line orientation indicating no significant anisotropy in mobilities of edge and screw segments. The shear-modulus-normalized CRSS of the HEA is not exceptionally high compared to those of certain concentrated binary FCC solid solutions. Its rough magnitude calculated using the Fleischer/Labusch models corresponds to that of a hypothetical binary with the elastic constants of our HEA, solute concentrations of 20–50 at.%, and atomic size misfit of ~4%.