The contribution of kinematic hardening to the overall strain hardening of a high entropy alloy (HEA) was investigated for the first time ever. It was assessed for a single-phase equiatomic CoCrFeMnNi alloy based on a study of the Bauschinger effect. The observed occurrence of high back stresses signifies substantial kinematic hardening. We attribute it to the low probability of cross-slip in this HEA which, however, rises in the process of straining. A model that captures the mentioned effects was proposed and validated.