Tissue engineering offers a great potential in regenerative dentistry and to this end, three dimensional (3D) bioprinting has been emerging nowadays to enable the incorporation of living cells into the biomaterials (such a mixture is referred as a bioink in the literature) to create scaffolds. However, the bioinks available for scaffold bioprinting are limited, particularly for dental tissue engineering, due to the complicated, yet compromised, printability, mechanical and biological properties simultaneously imposed on the bioinks. This paper presents our study on the development of a novel bioink from carboxymethyl chitosan (CMC) and alginate (Alg) for bioprinting scaffolds for enamel tissue regeneration. CMC was used due to its antibacterial ability and superior cell interaction properties, while Alg was added to enhance the printability and mechanical properties as well as to regulate the degradation rate. The bioinks with three mixture ratios of Alg and CMC (2–4, 3–3 and 4–2) were prepared, and then printed into the calcium chloride crosslinker solution (100 mM) to form a 3D structure of scaffolds. The printed scaffolds were characterized in terms of structural, swelling, degradation, and mechanical properties, followed by their in vitro characterization for enamel tissue regeneration. The results showed that the bioinks with higher concentrations of Alg were more viscous and needed higher pressure for printing; while the printed scaffolds were highly porous and showed a high degree of printability and structural integrity. The hydrogels with higher CMC ratios had higher swelling ratios, faster degradation rates, and lower compressive modulus. Dental epithelial cell line, HAT-7, could maintain high viability in the printed constructs after 1, 7 and 14 d of culture. HAT-7 cells were also able to maintain their morphology and secrete alkaline phosphatase after 14 d of culture in the 3D printed scaffolds, suggesting the capacity of these cells for mineral deposition and enamel-like tissue formation. Among all combinations Alg4%–CMC2% and in a less degree 2%Alg–4%CMC showed the higher potential to promote ameloblast differentiation, Ca and P deposition and matrix mineralization in vitro. Taken together, Alg-CMC has been illustrated to be suitable to print scaffolds with dental epithelial cells for enamel tissue regeneration.