We report the synthesis of superconducting MgB2 nanowires using a two-step process involving the sol-gel technique and heat treatment in pure argon atmosphere at 820 degrees C. High resolution transmission electron microscopy revealed that MgB2 nanowires are single crystalline. The nanowires are 0.5-1.0 mu m long with diameters similar to 50-100 nm. Superconductivity in these nanowires has been confirmed by DC magnetization measurements indicating the superconducting transition temperature similar to 38 K.