This paper addresses the problem of driving a surface vessel along a desired spatial path. A nonlinear adaptive controller is designed that yields convergence of the trajectories of the closed loop system to the path in the presence of constant unknown ocean currents and parametric model uncertainty. Controller design builds on Lyapunov based techniques and backstepping. The controller derived implicitly compensates for the effect of the ocean current without the need for direct measurements of its velocity. An illustrative simulation example is presented and discussed.