An apparatus for creep indentation of individual adherent cells was designed, developed, and experimentally validated. The creep cytoindentation apparatus (CCA) can perform stress-controlled experiments and measure the corresponding deformation of single anchorage-dependent cells. The apparatus can resolve forces on the order of 1 nN and cellular deformations on the order of 0.1 μm. Experiments were conducted on bovine articular chondrocytes using loads on the order of 10 nN. The experimentally observed viscoelastic behavior of these cells was modeled using the punch problem and standard linear solid. The punch problem yielded a Young’s modulus of 1.11±0.48 kPa. The standard linear solid model yielded an instantaneous elastic modulus of 8.00±4.41 kPa, a relaxed modulus of 1.09±0.54 kPa, an apparent viscosity of 1.50±0.92 kPa-s, and a time constant of 1.32±0.65 s. To our knowledge, this is the first time that stress-controlled indentation testing has been applied at the single cell level. This methodology represents a new tool in understanding the mechanical nature of anchorage-dependent cells and mechanotransductional pathways.