Three-dimensional (3D) bioprinting of hybrid constructs is a promising biofabrication method for cartilage tissue engineering because a synthetic polymer framework and cell-impregnated hydrogel provide structural and biological features of cartilage, respectively. During bioprinting, impregnated cells may be subjected to high temperatures (caused by the adjacent melted polymer) and process-induced mechanical forces, potentially compromising cell function. This study addresses these biofabrication issues, evaluating the heat distribution of printed polycaprolactone (PCL) strands and the rheological property and structural stability of alginate hydrogels at various temperatures and concentrations. The biocompatibility of parameters from these studies was tested by culturing 3D hybrid constructs bioprinted with primary cells from embryonic chick cartilage. During initial two-dimensional culture expansion of these primary cells, two morphologically and molecularly distinct cell populations (“rounded” and “fibroblastic”) were isolated. The biological performance of each population was evaluated in 3D hybrid constructs separately. The cell viability, proliferation, and cartilage differentiation were observed at high levels in hybrid constructs of both cell populations, confirming the validity of these 3D bioprinting parameters for effective cartilage tissue engineering. Statistically significant performance variations were observed, however, between the rounded and fibroblastic cell populations. Molecular and morphological data support the notion that such performance differences may be attributed to the relative differentiation state of rounded versus fibroblastic cells (i.e., differentiated chondrocytes vs. chondroprogenitors, respectively), which is a relevant issue for cell-based tissue engineering strategies. Taken together, our study demonstrates that bioprinting 3D hybrid constructs of PCL and cell-impregnated alginate hydrogel is a promising approach for cartilage tissue engineering.