Three-dimensional (3D) bioprinting has been proven to be the chosen method of fabricating tissue implants and organ models because it can replicate the desired intricate geometries with great accuracy and precision. However, it faces unique challenges distinct from other 3D printing methods, particularly concerning the viscosity of bioink and the multidimensionality of biological structures. There are three fundamental challenges to bioprint any functional tissue, namely 1) achieving shape fidelity for structures in the biological dimensional range with native mechanical properties, 2) ensuring dense vascularization, and 3) attaining cell density akin to native tissue. Despite exploring diverse combinations of bioink materials, achieving consistent success and reproducibility remains challenging. We focused on attaining shape fidelity; here, we have described a 3D printing methodology where chitosan was dissolved in an alkaline solvent, enabling crosslinking with water. Rheological assessment of the bioink using the Power law model illustrated its shear-thinning properties, which is essential for extrusion-based 3D bioprinting. Printing parameters were optimized. The 3D bioprinting was carried out within a support hydrogel comprising thermoresponsive gelatin showing Bingham rheology. This supportive material prevented the collapse of the printed structures. Post-printing, the structures were crosslinked by pouring 40ºC water into the print container, simultaneously melting the support medium, and facilitating the recovery of the 3D bioprinted complex structure like a tri-leaflet heart valve, etc. The printed dimensional accuracy was in the range of .stl file dimensions. The mechanical properties of the printed structures fall in the range of native human soft tissue, i.e. 0.1KPa–1MPa. The degradation study described the variation in stability of the 3D bioprinted construct at different incubation conditions. Utilizing chitosan-based bioink and support-driven 3D bioprinting presents a promising avenue for creating intricate vascular structures, propelling advancements in tissue engineering and diverse biomedical applications.