Cartilage tissue equivalents formed from hydrogels containing chondrocytes could provide a solution for replacing damaged cartilage. Previous approaches have often utilized elastic hydrogels. However, elastic stresses may restrict cartilage matrix formation and alter the chondrocyte phenotype. Here we investigated the use of viscoelastic hydrogels, in which stresses are relaxed over time and which exhibit creep, for three-dimensional (3D) culture of chondrocytes. We found that faster relaxation promoted a striking increase in the volume of interconnected cartilage matrix formed by chondrocytes. In slower relaxing gels, restriction of cell volume expansion by elastic stresses led to increased secretion of IL-1β, which in turn drove strong up-regulation of genes associated with cartilage degradation and cell death. As no cell-adhesion ligands are presented by the hydrogels, these results reveal cell sensing of cell volume confinement as an adhesion-independent mechanism of mechanotransduction in 3D culture, and highlight stress relaxation as a key design parameter for cartilage tissue engineering.