A semiclassical method for treating tunneling in molecular collisions is presented. The procedure incorporates tunneling into standard classical trajectory simulations. The tunneling rate is computed by calculating the JWKB tunneling probabilities along predefined tunneling paths at the classical turning points which are determined by classical trajectory calculations. The method is illustrated for the collinear H+H-2 atom-exchange reaction on the Porter-Karplus surface. The calculated reaction probabilities are in good agreement with the quantum-mechanical values, and are in fact as good as the results obtained from more sophisticated semiclassical treatments such as the S-matrix theory and the instanton model. The method can readily be extended to higher dimensions.