Starting from the type IIB string on the Z orbifold, we construct some chiral open-string vacua with N = 1 supersymmetry in four dimensions, The Chan-Paton group depends on the (quantized) NS-NS antisymmetric tenser. The largest choice, SO(8) x SU(12) x U(1), has an anomalous U(1) factor whose gauge boson acquires a mass of the order of the string scale. The corresponding open-string spectrum comprises only Neumann strings and includes three families of chiral multiplets in the (8, 12*) + (1, 66) representation. A comparison is drawn with a heterotic vacuum with non-standard embedding, and some properties of the low-energy effective field theory are discussed.