Naturally deformed dunite cores with a preexisting crystallographic preferred orientation (CPO), collected from a shear zone in the Josephine peridotite (southwest Oregon, USA), were deformed experimentally in triaxial compression. The compression axis was varied relative to the CPO geometry to measure the anisotropy in viscosity of these rocks. Deformation experiments were performed in a gas-medium apparatus at three constant displacement-rate steps, at a temperature of 1250 °C and a confining pressure of 300 MPa. Cores were dehydrated at 1200 °C in a controlled CO/CO2 atmosphere prior to deformation to achieve nominally dry conditions. Data from individual experiments were fit by a power-law, yielding a stress exponent of n ≈ 3.6, indicative of deformation by dislocation creep. The maximum difference in viscosity was a factor of 2.6 at constant stress. The CPO of the olivine grains was measured after deformation by electron backscatter diffraction (EBSD). The flow stress correlated with the mean Schmid factor (or resolved shear stress) on the easiest dislocation slip systems, calculated from grain orientations determined from EBSD analyses. Analysis of our data with a simplified effective-medium model, which incorporated constraints from published single-crystal flow laws, demonstrated the link between CPO and anisotropy in viscosity. Predictions from viscoplastic self-consistent (VPSC) models support our simplified analysis of the measured anisotropy.