The main purpose of this paper is to derive a wall law for a flow over a very rough surface. We consider a viscous incompressible fluid filling a 3-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a very rough wall. The latter consists in a plane wall covered with periodically distributed asperities which size depends on a small parameter ε>0 and with a fixed height. We assume that the flow is governed by the stationary Stokes equations. Using asymptotic expansions and boundary layer correctors we construct and analyze an asymptotic approximation of order O(ε3/2−γ) (γ>0 being arbitrary small) in the H1-norm for the velocity and in the L2-norm for the pressure. We derive an effective boundary condition of Navier type, then expressing the boundary layer terms in terms of the homogenized solution and the solution of a cell problem we obtain an effective approximation in the whole domain of the flow.