Thermoelectric Bi2Te3 based bulk materials are widely used for solid-state refrigeration and power-generation at room temperature. For low-dimensional and nanostructured thermoelectric materials an increase of the thermoelectric figure of merit ZT is predicted due to quantum confinement and phonon scattering at interfaces. Therefore, the fabrication of Bi2Te3 nanowires, thin films, and nanostructured bulk materials has become an important and active field of research. Stoichiometric Bi2Te3 nanowires with diameters of 50-80 nm and a length of 56 mu m are grown by a potential-pulsed electrochemical deposition in a nanostructured Al2O3 matrix. By transmission electron microscopy (TEM), dark-field images together with electron diffraction reveal single-crystalline wires, no grain boundaries can be detected. The stoichiometry control of the wires by high-accuracy, quantitative enegy-dispersive X-ray spectroscopy (EDX) in the TEM instrument is of paramount importance for successfully implementing the growth technology. Combined electron diffraction and EDX spectroscopy in the TEM unambiguously prove the correct crystal structure and stoichiometry of the Bi2Te3 nanowires. X-ray and electron diffraction reveal growth along the [110] and [210] directions and the c axis of the Bi2Te3 structure lies perpendicular to the wire axis. For the first time single crystalline, stoichiometric Bi2Te3 nanowires are grown that allow transport in the basal plane without being affected by grain boundaries.