The simplified thermodynamic perturbation theory-dimer (STPT-D) equation of state is generalized to mixtures of hard-sphere chains. The generalized equation contains no additional adjustable parameters, and it can be used for hard-sphere chain mixtures containing components with either identical or dissimilar hard-sphere segments. The compressibility factor predicted by the STPT-D equation of state is compared with molecular simulation data for several hard-sphere chain mixtures. Good agreement with simulation data is obtained when the ratio of hard-sphere segment diameters for the component chains is <2. For these mixtures the average absolute deviation between theory and simulation is typically 0.35%-3.5%. The accuracy of the STPT-D equation compares favorably with the results obtained for other, more complicated, hard-sphere chain equations of state.