We have investigated the formation of tungsten oxide nanowires under different chemical vapor deposition (CVD) conditions. We find that exposure of oxidized tungsten films to hydrogen and methane at 900 degrees C leads to the formation of a dense array of typically 10 nm diameter nanowires. Structural and chemical analysis shows that the wires are crystalline WO3. We propose a chemically driven whisker growth mechanism in which interfacial strain associated with the formation of tungsten carbide stimulates nanowire growth. This might be a general concept, applicable also to other nanowire systems.