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This paper addresses the position tracking control design problem for an autonomous underwater vehicle (AUV). The vehicle dynamics is subjected to a non-holonomic velocity constraint arising due to fluid interactions, resulting in a differential- algebraic equation (DAE) formulation for the equations of motion. A reduced order state-space model in a chained form is derived after solving the constraint force. A hierarchical geometric control law is designed for tracking the position of the centre of mass, via this chained form so that the tracking error is almost globally exponentially stable. Simulations on a planar AUV model have been presented to illustrate the performance of the control law.