The AR2O4 family (R = rare earth) have recently been attracting interest as a new series of frustrated magnets, with the magnetic R atoms forming zigzag chains running along the c-axis. We have investigated polycrystalline BaNd2O4 with a combination of magnetization, heat capacity, and neutron powder diffraction (NPD) measurements. Magnetic Bragg peaks are observed below TN = 1.7 K, and they can be indexed with a propagation vector of k = (0 1/2 1/2). The signal from magnetic diffraction is well described by long-range ordering of only one of the two types of Nd zigzag chains, with collinear up-up-down-down intrachain spin configurations (Double Néel state). Furthermore, low temperature magnetization and heat capacity measurements reveal two magnetic field-induced spin transitions at 2.75 T and 4 T for T = 0.46 K. The high field phase is paramagnetic, while the intermediate field state may arise from a spin transition of the long-range ordered Nd chains. One possible candidate for the field-induced ordered state corresponds to an up-up-down intrachain spin configuration, as predicted for a classical J1-J2 Ising chain with a Double Néel ground state in zero field.