We report for the first time the chemical synthesis of free-standing single-crystal nanowires (NWs) of FeSi, the only transition-metal Kondo insulator and the host structure for ferromagnetic semiconductor Fe(x)Co(1-x)Si. Straight and smooth FeSi nanowires are produced on silicon substrates covered with a thin layer of silicon oxide through the decomposition of the single-source organometallic precursor trans-Fe(SiCl3)2(CO)4 in a simple chemical vapor deposition process. Unlike typical vapor-liquid-solid (VLS) NW growth, FeSi NWs form without the addition of metal catalysts, have no catalyst tips, and depend strongly on the surface employed. X-ray spectroscopy verifies the identity and the room-temperature metallic nature of FeSi NWs. Room-temperature electrical transport measurements using NW devices show an average resistivity of 210 micro Omega cm, similar to the value for bulk FeSi. Investigations into the low-temperature physical properties of the first one-dimensional Kondo insulator and the possible new NW growth mechanism are underway. This unique synthetic approach to FeSi NWs will be generally applicable to many other transition-metal silicides.