We study the problem of safe adaptation: given a model trained on a variety of past experiences for some task, can this model learn to perform that task in a new situation while avoiding catastrophic failure? This problem setting occurs frequently in real-world reinforcement learning scenarios such as a vehicle adapting to drive in a new city, or a robotic drone adapting a policy trained only in simulation. While learning without catastrophic failures is exceptionally difficult, prior experience can allow us to learn models that make this much easier. These models might not directly transfer to new settings, but can enable cautious adaptation that is substantially safer than naïve adaptation as well as learning from scratch. Building on this intuition, we propose risk-averse domain adaptation (RADA). RADA works in two steps: it first trains probabilistic model-based RL agents in a population of source domains to gain experience and capture epistemic uncertainty about the environment dynamics. Then, when dropped into a new environment, it employs a pessimistic exploration policy, selecting actions that have the best worst-case performance as forecasted by the probabilistic model. We show that this simple maximin policy accelerates domain adaptation in a safety-critical driving environment with varying vehicle sizes. We compare our approach against other approaches for adapting to new environments.