We consider task and motion planning in complex dynamic environments for problems expressed in terms of a set of Linear Temporal Logic (LTL) constraints, and a reward function. We propose a methodology based on reinforcement learning that employs deep neural networks to learn low-level control policies as well as task-level option policies. A major challenge in this setting, both for neural network approaches and classical planning, is the need to explore future worlds of a complex and interactive environment. To this end, we integrate Monte Carlo Tree Search with hierarchical neural net control policies trained on expressive LTL specifications. This paper investigates the ability of neural networks to learn both LTL constraints and control policies in order to generate task plans in complex environments. 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 given rules of the road.