We report a search for a dark vector gauge boson U' that couples to quarks in the decay chain D*(+) -> D-0 pi(+), D-0 -> K-S(0) eta, eta -> U'gamma, U' -> pi(+)pi- No signal is found and we set a mass-dependent limit on the baryonic fine structure constant of 10(-3)-10(-2) in the U' mass range of 290 to 520 MeV/c(2). This analysis is based on a data sample of 976 fb(-1) collected by the Belle experiment at the KEKB asymmetric-energy e(+)e(-) collider.