With the advent of applied 3D fields in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous slowing down, and pitch angle scattering are modeled with the ADAS atomic physics database. Elementary benchmark calculations are presented to verify the collisionless particle orbits, NBI model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.