We report the first ab initio calculation of the nuclear-structure-dependent radiative correction \(\delta{NS}\) to the \(^{10}\)C\(→\)\(^{10}\)B superallowed transition, computed with the no-core shell model and chiral effective field theory. We obtain \(\delta_{NS}=−0.422 (29)_{nuc} (12)_{n,el}\) with a 1.6-times reduction in the total uncertainty when compared to the current literature estimate based on the shell model and Fermi gas picture. This Letter paves the way for a precise determination of \(V_{ud}\) from superallowed beta decays within a systematically improvable framework.