<p>A modified form of Legendre-Gauss orthogonal direct collocation is developed for solving optimal control problems whose solutions are nonsmooth due to control discontinuities. This new method adds switch time variables, control variables, and collocation conditions at both endpoints of a mesh interval – features that are absent from the standard Legendre-Gauss orthogonal collocation. By modifying the search space of the resulting nonlinear programming problem, this approach effectively identifies the locations of nonsmoothness in the optimal control solution. The transformed adjoint system of the modified Legendre-Gauss collocation method is also derived and shown to satisfy a discrete form of the continuous variational necessary conditions for optimality. The method is motivated via a control-constrained triple-integrator minimum-time optimal control problem where the solution possesses a two-switch bang-bang optimal control structure. Finally, the method developed in this paper is compared with existing Gaussian quadrature collocation methods and is shown to accurately solve optimal control problems with discontinuous controls.</p>