Meta-learning, or learning-to-learn, has proven to be a successful strategy in attacking problems in supervised learning and reinforcement learning that involve small amounts of data. State-of-the-art solutions involve learning an initialization and/or learning algorithm using a set of training episodes so that the meta learner can generalize to an evaluation episode quickly. These methods perform well but often lack good quantification of uncertainty, which can be vital to real-world applications when data is lacking. We propose a meta-learning method which efficiently amortizes hierarchical variational inference across tasks, learning a prior distribution over neural network weights so that a few steps of Bayes by Backprop will produce a good task-specific approximate posterior. We show that our method produces good uncertainty estimates on contextual bandit and few-shot learning benchmarks.