The classical trajectory method (also called molecular dynamics) is the most widely used method for ensemble averaging and calculating rate constants of complex dynamical systems; however it has the serious drawback of not allowing tunneling. Here, we show how to include tunneling efficiently in real-time classical trajectories by using the army ants algorithm for quantum mechanical rare event sampling and partially optimized semiclassical tunneling paths based on valence internal coordinates. Three examples, HN2 dissociation and two kinds of HCOH isomerizations, are used to illustrate the tunneling method. We show that the army ants tunneling algorithm is very efficient (even lower computational costs than calculations without tunneling) and yields physically reasonable rate constants. The new algorithm is straightforward to include in any molecular dynamics package, and it allows sampling of regions of phase space that are classically inaccessible but that may lead to different products or different energy distributions than are populated by non-tunneling processes.