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We ask whether everyday open-world monocular videos can be turned into reusable 4D interaction primitives: articulated hand motion, object shape with 6D pose over time, and the when/where of contact. Such a capability would enable scalable mining of real interactions and, beyond reconstruction, support scene-aware synthesis and planning. However, reconstructing hand-object interaction (HOI) from challenging monocular videos remains difficult: methods often assume known objects or curated scenes, and separately estimated hands and objects easily become misaligned under clutter, occlusion, and unseen object geometries. Targeting this setting, we present CHOIR, a Contact-aware HOI Reconstruction framework for a monocular camera, using contact as an explicit coupling signal between hands and objects. CHOIR first initializes a coarse, contact-agnostic 4D HOI sequence from open-world visual priors. It then introduces a generative HOI spatial rectification module to predict ray-depth corrections and rectify hand-object relative placement, then derive initial per-frame contact correspondences on the rectified geometry. Last, a contact-aware joint optimization with dynamically updated contact constraints enforces geometric, temporal, and contact consistency. Experiments on controlled and challenging videos show that CHOIR improves object reconstruction, physical plausibility, and temporal consistency over state-of-the-art methods.