A new method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method developed in this paper employs a modified form of the Legendre-Gauss-Radau (LGR) orthogonal direct collocation method in which an additional variable and two additional constraints are included at the end of a mesh interval. The additional variable is the switch time where a discontinuity occurs. The two additional constraints are a collocation condition on each differential equation that is a function of control along with a control constraint at the endpoint of the mesh interval that defines the location of the nonsmoothness. These additional constraints modify the search space of the NLP in a manner such that an accurate approximation to the location of the nonsmoothness is obtained. An example with a nonsmooth solution is used throughout the paper to illustrate the improvement of the method over the standard Legendre-Gauss-Radau collocation method.