Three-dimensional (3D) in vitro models capturing both the structural and dynamic complexity of the in vivo situation are in great demand as an alternative to animal models. Despite tremendous progress in engineering complex tissue/organ models in the past decade, approaches that support the required freedom in design, detail and chemistry for fabricating truly 3D constructs have remained limited. Here, we report a stereolithographic high-resolution 3D printing technique utilizing poly(ethylene glycol) diacrylate (PEGDA, MW 700) to manufacture diffusion-open and mechanically stable hydrogel constructs as self-contained chips, where confined culture volumes are traversed and surrounded by perfusable vascular-like networks. An optimized resin formulation enables printing of hydrogel chips holding perfusable microchannels with a cross-section as small as 100 μm × 100 μm, and the printed microchannels can be steadily perfused for at least one week. In addition, the integration of multiple independently perfusable and structurally stable channel systems further allows for easy combination of different bulk material volumes at exact relative spatial positions. We demonstrate this structural and material flexibility by embedding a highly compliant cell-laden gelatin hydrogel within the confines of a 3D printed resilient PEGDA hydrogel chip of intermediate compliance. Overall, our proposed strategy represents an automated, cost-effective and high resolution technique to manufacture complex 3D constructs containing microfluidic perfusion networks for advanced in vitro models.