The chain-like system Ba(3)Cu(3)Sc(4)O(12) has potentially interesting magnetic properties due to the presence of Cu(2+) and a structure-suggested low dimensionality. We present magnetization M versus magnetic field H and temperature T, T- and H-dependent heat-capacity C(p), (45)Sc nuclear magnetic resonance (NMR), muon spin rotation (μSR), neutron diffraction measurements and electronic structure calculations for Ba(3)Cu(3)Sc(4)O(12). The onset of magnetic long-range antiferromagnetic (AF) order at T(N) ∼ 16 K is consistently evidenced from the whole gamut of our data. A significant sensitivity of T(N) to the applied magnetic field H (T(N) ∼ 0 K for H = 70 kOe) is also reported. Coupled with a ferromagnetic Curie-Weiss temperature (θ(CW) ∼ 65 K) in the susceptibility (from a 100 to 300 K fit), it is indicative of competing ferromagnetic and antiferromagnetic interactions. These indications are corroborated by our density functional theory based electronic structure calculations, where we find the presence of significant ferromagnetic couplings between some copper ions whereas AF couplings were present between some others. Our experimental data, backed by our theoretical calculations, rule out the one-dimensional magnetic behavior suggested by the structure and the observed long-range order is due to the presence of non-negligible magnetic interactions between adjacent as well as next-nearest chains.