In this work, we introduce the Virtual In-Hand Eye Transformer (VIHE), a novel method designed to enhance 3D manipulation capabilities through action-aware view rendering. VIHE autoregressively refines actions in multiple stages by conditioning on rendered views posed from action predictions in the earlier stages. These virtual in-hand views provide a strong inductive bias for effectively recognizing the correct pose for the hand, especially for challenging high-precision tasks such as peg insertion. On 18 manipulation tasks in RLBench simulated environments, VIHE achieves a new state-of-the-art, with a 12% absolute improvement, increasing from 65% to 77% over the existing state-of-the-art model using 100 demonstrations per task. In real-world scenarios, VIHE can learn manipulation tasks with just a handful of demonstrations, highlighting its practical utility. Videos and code implementation can be found at our project site: https://vihe-3d.github.io.

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