Catalysis of the reaction: beta-D-glucuronosyl-(1,4)-N-acetyl-alpha-D-glucosaminyl-proteoglycan + UDP-N-acetyl-D-glucosamine = N-acetyl-alpha-D-glucosaminyl-(1,4)-beta-D-glucuronosyl-(1,4)-N-acetyl-alpha-D-glucosaminyl-proteoglycan + UDP.