The temperature dependence of the electrical resistivity along the a and b axes of YBa2Cu3O6.9 has been measured in high-purity fully-detwinned single crystals. Below 300K, rho(a)(T) is found to be perfectly linear, while rho(b)(T) reveals a distinct upward curvature. Viewing the b-axis conductivity as the sum of parallel conductivities in the CuO2 planes and along the Cu-O chains, a T-2 dependence for the chain resistivity is obtained. Such a dependence, also observed in quasi-1D conductors, sheds light on a number of hitherto ill-identified deviations from linearity reported recently. Above 300K, there is a steep linear increase in rho(chain)(T), most likely associated with the increased oxygen mobility.