Polymerizes chitin, a structural polymer of the cell wall and septum, by transferring the sugar moiety of UDP-GlcNAc to the non-reducing end of the growing chitin polymer. [(1->4)-N-acetyl-beta-D-glucosaminyl](n) + UDP-N-acetyl-alpha-D-glucosamine = [(1->4)-N-acetyl-beta-D-glucosaminyl](n+1) + H(+) + UDP A constitutive cytoplasmic pool is present that localizes to intracellular microvesicles termed chitosomes. Chitosomes constitute a separate secretory route distinct from the typical secretory pathway and serve as a vehicle for delivering the enzyme to the sites on the cell surface where polysaccharide sythesis takes place (By similarity). Localizes to septa of yeast-like cells and to the basal septum separating the living tip cell from the vacuolated part in hyphae. Belongs to the chitin synthase family. Class III subfamily.