We construct spherically symmetric thin-shell wormholes supported by a generalized Chaplygin gas in Born–Infeld electrodynamics coupled to Einstein gravity, and we analyze their stability under radial perturbations. For different values of the Born–Infeld parameter and the charge, we compare the results with those obtained in a previous work for Maxwell electrodynamics. The stability region in the parameter space reduces and then disappears as the value of the Born–Infeld parameter is modified in the sense of a larger departure from Maxwell theory.