Biocompatible polymers that form thermoreversible supramolecular hydrogels have gained great interest in biomaterials research and tissue engineering. When favorable rheological properties are achieved at the same time, they are particularly promising candidates as material that allow for the printing of cells, so-called bioinks. We synthesized a novel thermogelling block copolymer and investigated the rheological properties of its aqueous solution by viscosimetry and rheology. The polymers undergo thermogelation between room temperature and body temperature, form transparent hydrogels of surprisingly high strength (G' > 1000 Pa) and show rapid and complete shear recovery after stress. Small angle neutron scattering suggests an unusual bicontinuous sponge-like gel network. Excellent cytocompatibility was demonstrated with NIH 3T3 fibroblasts, which were incorporated and bioplotted into predefined 3D hydrogel structures without significant loss of viability. The developed materials fulfill all criteria for future use as bioink for biofabrication.