Catalyzes the reversible phosphorolysis of chitobiose (N,N'-diacetylchitobiose or (GlcNAc)(2)) into alpha-GlcNAc-1-phosphate and GlcNAc with inversion of the anomeric configuration. N,N'-diacetylchitobiose + phosphate = N-acetyl-alpha-D-glucosamine 1-phosphate + N-acetyl-D-glucosamine Optimum pH is 6.5-7.0. Optimum temperature is 20-37 degrees Celsius. Homodimer. Belongs to the glycosyl hydrolase 94 family.