The naturally occurring α-chitin biopolymer was employed for the immobilisation of copper(I) ion, resulting into a new bioconjugate complex, namely, Cu(I)-α-chitin (CuI-CHT) with catalytic efficiency in copper-catalysed azide-alkyne cycloaddition reactions (click chemistry, CuAAC). The prepared catalyst was characterised by using spectroscopic and analytical methods such as Fourier-transform infrared (FT-IR), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX), X-ray diffraction (XRD) and inductively coupled plasma (ICP) analysis. The catalytic activity of CuI-CHT was investigated in the [3 + 2] cycloaddition reactions of alkynes and organic azides for the regioselective click of 1,4-disubstituted-1,2,3-triazole derivatives in water at room temperature. The catalytic results indicate that the prepared CuI-CHT catalyst led to a high yield with a regioselective synthesis of the corresponding 1,4-disubstituted-1,2,3-triazoles under strict click conditions. The reusability and simple recovery of this catalyst make it a suitable sustainable catalyst for CuAAC reactions.