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High-entropy alloys (HEAs) composed of multiple principal elements have been shown to offer improved radiation resistance over their elemental or dilute-solution counterparts. Using NiCoFeCrMn HEA as a model, here we introduce carbon and nitrogen interstitial alloying elements to impart chemical heterogeneities in the form of the local chemical order (LCO) and associated compositional variations. Density functional theory simulations predict chemical short-range order (CSRO) (nearest neighbors and the next couple of atomic shells) surrounding C and N, due to the chemical affinity of C with (Co, Fe) and N with (Cr, Mn). Atomic-resolution chemical mapping of the elemental distribution confirms marked compositional variations well beyond statistical fluctuations. Ni+ irradiation experiments at elevated temperatures demonstrate a remarkable reduction in void swelling by at least one order of magnitude compared to the base HEA without C and N alloying. The underlying mechanism is that the interstitial-solute-induced chemical heterogeneities roughen the lattice as well as the energy landscape, impeding the movements of, and constraining the path lanes for, the normally fast-moving self-interstitials and their clusters. The irradiation-produced interstitials and vacancies therefore recombine more readily, delaying void formation. Our findings thus open a promising avenue towards highly radiation-tolerant alloys.