Summary: The low-energy \(D=4\), \(N=1\) effective action of the strongly coupled heterotic string is explicitly computed by compactifying the Hořava-Witten theory on the deformed Calabi-Yau three-fold solution due to Witten. It is shown that, to order \(\kappa^{2/3}\), the Kähler potential is identical to that of the weakly coupled theory. Furthermore, the gauge kinetic functions are directly computed to order \(\kappa^{4/3}\) and shown to receive a non-vanishing correction. Also, we compute gauge matter terms in the Kähler potential to the order \(\kappa^{4/3}\) and find a non-trivial correction to the dilaton term. Part of those corrections arise from background fields that depend on the orbifold coordinate and are excited by four-dimensional gauge field source terms.