Potential energy surfaces are obtained for singlet H-3(+) in magnetic fields of up to 2350 T. The magnetic interaction was treated by first order perturbation theory and the interaction terms computed ab initio. They were then fitted to a functional form and added to a recent, highly accurate adiabatic potential energy surface. In its most stable orientation, the molecule is arranged such that the magnetic field vector is in the molecular plane. The most stable configuration is no longer D-3h as in the field-free case, but C-2v, though the stabilization energy is extremely small, of the order of 0.01 cm(-1) for a 2350 T field. Finally, we have calculated, for a range of magnetic field strengths and orientations, all the vibrational eigenvalues that are below the barrier to linearity in the field free case.