Concolic execution and fuzzing are two complementary coverage-based testing techniques. How to achieve the best of both remains an open challenge. To address this research problem, we propose and evaluate Legion. Legion uses a variation of the Monte Carlo tree search (MCTS) framework from the AI literature to treat automated test generation as a problem of sequential decision-making under uncertainty. Its best-first search strategy provides a principled way to learn the most promising program states to investigate at each search iteration, based on observed rewards from previous iterations. Legion incorporates a form of directed fuzzing that we call approximate path-preserving fuzzing (APPFuzzing) to investigate program states selected by MCTS. APPFuzzing serves as the Monte Carlo simulation technique and is implemented by extending prior work on constrained sampling. We evaluate Legion against competitors in Test-Comp 2020, as well as measuring its sensitivity to hyperparameters, demonstrating its effectiveness on a wide variety of input programs.