We consider the elliptic equation -Delta u + u = 0 in a bounded, smooth domain Omega in R-2 subject to the nonlinear Neumann boundary condition partial derivative u/partial derivative v = lambda ue(u2), where v denotes the outer normal vector of partial derivative Omega. Here lambda > 0 is a small parameter. For any lambda small we construct positive solutions concentrating, as lambda -> 0, around points of the boundary of Omega.