Autonomously discovering temporally extended actions, or skills, is a longstanding goal of hierarchical reinforcement learning. We propose a new algorithm that combines skill chaining with deep neural networks to autonomously discover skills in high-dimensional, continuous domains. The resulting algorithm, deep skill chaining, constructs skills with the property that executing one enables the agent to execute another. We demonstrate that deep skill chaining significantly outperforms both non-hierarchical agents and other state-of-the-art skill discovery techniques in challenging continuous control tasks.