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For robots to assist, serve, and collaborate with humans, they must not only interpret human requests conveyed through language and multimodal intentional cues, but also execute long-horizon tasks that interleave navigation and manipulation. In this paper, we introduce HEIR, a resource for studying how to Harness Egocentric Intent for Human-Robot Interaction. HEIR pairs human speech, measured gaze, and egocentric video with robot observations and teleoperated navigation-manipulation trajectories, while each session preserves successive episodes, with each request fulfilled through multiple execution subtasks. The captured data, together with human-authored annotations, support the study of intent grounding, execution planning, and task completion within a unified interaction setting. To demonstrate the value of HEIR, we conduct extensive offline experiments to evaluate how models benefit from additional human-centric context across these tasks, together with real-robot experiments that assess execution task completion. HEIR thus provides a valuable resource for studying user-centric robot interaction in naturalistic household environments. Our demo and dataset are available online.