Organ-on-chip (OoC) platforms are increasingly adopted for predictive in vitro testing. However, most remain limited by soft-lithography-derived 2.5D microfluidic architectures and non-physiological rigid materials, or bioprinting approaches that require complex and failure-prone post-fabrication assembly. Here, we present a versatile approach that integrates tomographic volumetric additive manufacturing (TVAM) directly within preassembled microfluidic chips, enabling rapid, contactless fabrication of freeform 3D OoCs. Leveraging our open-source optical simulation framework, Dr.TVAM, we perform TVAM in custom-designed chips, eliminating post-printing manual assembly steps that commonly lead to leakage, contamination, and poor reproducibility. This strategy, termed TVAM-in-a-chip, supports the generation of diverse 3D channel architectures in multiple biocompatible photoresins spanning a wide range of chemistries and mechanical properties, including cell-laden formulations. We demonstrate multi-channel designs, compatibility with confocal imaging, and dynamic culture of epithelial and endothelial models. Overall, TVAM-in-a-chip overcomes key limitations of current OoC technologies and paves the way for a new generation of scalable, biomimetic 3D platforms for advanced in vitro modeling.