Development of biomaterial-based bioinks is critical for replacement and/or regeneration of tissues and organs by three-dimensional (3D) printing techniques. However, the number of 3D-printable biomaterials in practical use remains limited despite the rapid development of 3D printing techniques. Controlling the flow properties of bioinks and mechanical properties of the resultant printed objects is key considerations in the design of biomaterial-based bioinks for practical applications. In this study, a printable hydrogel comprising biocompatible polysaccharides that has potential for cartilage regeneration via tissue engineering approaches was designed. Self-healing hydrogels were prepared from partially oxidized hyaluronate (OHA) and glycol chitosan (GC) in the presence of adipic acid dihydrazide (ADH). The self-healing ability of OHA/GC/ADH hydrogels was attributed to the combination of two dynamic bonds in the gels, including imine bonds obtained via a Schiff base reaction between OHA and GC, as well as acylhydrazone bonds formed by the reaction between OHA and ADH. The OHA/GC/ADH hydrogels did not require any postgelation or additional cross-linking processes for use in the fabrication of 3D constructs using an extrusion-based 3D printer. The concentrations and molecular weights of the constituent polymers were found to be critical parameters affecting the flow and mechanical properties of the self-healing hydrogels, which showed great potential as bioinks for fabricating cell-laden structures using a 3D printer. The expression of chondrogenic marker genes such as SOX-9 and collagen type II of ATDC5 cells encapsulated in the OHA/GC/ADH hydrogel was not significantly affected by the printing process. This self-healing hydrogel system may have the potential in tissue engineering applications, including cartilage regeneration.