A reliable hydrogen-based energy technology requires promising materials for safe storage and transport of hydrogen. Here, the storage of hydrogen in the organic polymer poly(3,4-ethylenedioxythiophene) (PEDOT) is explored using density functional theory calculations. It is demonstrated that hydrogen chemisorption on PEDOT is feasible with the maximum gravimetric uptake of similar to 2.8 wt % in ambient condition, whereas physisorption is possible only at very low temperatures or at high pressure. The Gibbs absorption energies, electronic structure, and absorption spectra are calculated for the cases of chemisorption of a single hydrogen atom, a hydrogen pair, and hydrogen saturated chain for both neutral and oxidized PEDOT. Various experimental routes for PEDOT hydrogenations are discussed.