3D bioprinting may revolutionize the field of tissue engineering by allowing fabrication of bio-structures with a high degree of complexity, fine architecture and heterogeneous composition. The printing substances in these processes are mostly based on biomaterials and living cells. As such, they generally possess weak mechanical properties and thus must be supported during fabrication in order to prevent the collapse of large, volumetric multi-layered printouts. In this work, we characterize a uniquely formulated media used to support printing of extracellular matrix-based biomaterials. We show that a hybrid material, comprised of calcium-alginate nanoparticles and xanthan gum, presents superb qualities that enable printing at high resolution of down to 10 microns, allowing fabrication of complex constructs and cellular structures. This hybrid also presents an exclusive combination of desirable properties such as biocompatibility, high transparency, stability at a wide range of temperatures and amenability to delicate extraction procedures. Moreover, as fabrication of large, volumetric biological structures may require hours and even days to accomplish, we have demonstrated that the hybrid medium can support prolonged, precise printing for at least 18 h. All these qualities make it a promising support medium for 3D printing of tissues and organs.