We have measured the resistivity tensor in one nearly twin-free crystal and one twin-free crystal of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. The first crystal was grown with a large twin-free region. We removed the twins in the second crystal by applying a uniaxial stress. Using a modified Montgomery technique, we measured the electrical resistivities in all three crystal directions and found them to be linear in temperature above the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$. Our results for ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}}$ and ${\mathrm{\ensuremath{\rho}}}_{\mathit{b}}$ at room temperature are among the lowest that have been reported in the literature, indicating that our samples are of high quality. The ratio ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}}$/${\mathrm{\ensuremath{\rho}}}_{\mathit{b}}$ is independent of temperature between 150 and 275 K, and its value, 2.2\ifmmode\pm\else\textpm\fi{}0.2, indicates that the Cu-O chains contribute 60% of the current when the electric field is parallel to them, with the rest of the current being contributed by the Cu-O planes. This result, at zero frequency, is in good agreement with the recent conductivity at infrared frequencies obtained by Schlesinger et al.