Task and motion planning subject to Linear Temporal Logic (LTL) specifications in complex, dynamic environments requires efficient exploration of many possible future worlds. Model-free reinforcement learning has proven successful in a number of challenging tasks, but shows poor performance on tasks that require long-term planning. In this work, we integrate Monte Carlo Tree Search with hierarchical neural net policies trained on expressive LTL specifications. We use reinforcement learning to find deep neural networks representing both low-level control policies and task-level 'option policies' that achieve high-level goals. Our combined architecture generates safe and responsive motion plans that respect the LTL constraints. We demonstrate our approach in a simulated autonomous driving setting, where a vehicle must drive down a road in traffic, avoid collisions, and navigate an intersection, all while obeying rules of the road.