We present Reinforcement Learning via Auxiliary Task Distillation (AuxDistill), a new method that enables reinforcement learning (RL) to perform long-horizon robot control problems by distilling behaviors from auxiliary RL tasks. AuxDistill achieves this by concurrently carrying out multi-task RL with auxiliary tasks, which are easier to learn and relevant to the main task. A weighted distillation loss transfers behaviors from these auxiliary tasks to solve the main task. We demonstrate that AuxDistill can learn a pixels-to-actions policy for a challenging multi-stage embodied object rearrangement task from the environment reward without demonstrations, a learning curriculum, or pre-trained skills. AuxDistill achieves $2.3 \times$ higher success than the previous state-of-the-art baseline in the Habitat Object Rearrangement benchmark and outperforms methods that use pre-trained skills and expert demonstrations.