Catalysis of the reaction: UDP-N-acetyl-D-glucosamine + N-acetyl-D-glucosaminyl-diphosphodolichol = UDP + N,N''-diacetylchitobiosyldiphosphodolichol.
uridine diphosphoacetylglucosamine-dolichylacetylglucosamine pyrophosphate acetylglucosaminyltransferase activity