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Many of the studies on the entropy‐stabilized oxide (Mg_0.2Co_0.2Ni_0.2Cu_0.2Zn_0.2)O have been heavily application‐based. Previous works have studied effects of cation stoichiometry on the entropy‐driven reaction to form a single phase, but a fundamental exploration of the effects of anion stoichiometry and/or redox chemistry on electrical properties is lacking. Using near‐edge X‐ray absorption fine structure (NEXAFS) and electrical measurements, we show that oxidizing thin film samples of (Mg_0.2Co_0.2Ni_0.2Cu_0.2Zn_0.2)O affects primarily the valence of Co, leaving the other cations in this high‐entropy system unchanged. This oxidation increases electrical conduction in these thin films, which occurs via small polaron hopping mediated by the Co valence shift from 2+ to a mixed 2+/3+ state. In parallel, we show that bulk samples sintered in an oxygen‐rich atmosphere have a lower activation energy for electrical conduction than those equilibrated in a nitrogen (reducing) atmosphere. Combining feasible defect compensation scenarios with electrical impedance measurements and NEXAFS data, we propose a self‐consistent interpretation of Co redox‐mediated small polaron conduction as the dominant method of charge transfer in this system.