Optoelectronic measurements of carbon nanotube transistors have shown a wide variety of sensitivites to the incident light. Direct photocurrent processes compete with a number of extrinsic mechanisms. Here we show that visible light absorption in the silicon substrate generates a photovoltage that can electrically gate the nanotube device. The photocurrent induced by the changing gate voltage can be significantly larger than that due to direct electron-hole pair generation in the nanotube. The dominance of photogating in these devices is confirmed by the power and position dependence of the resulting photocurrent. The power dependence is strongly non-linear and photocurrents are measured through the device even when the laser illuminates up to 1~mm from the nanotube. ; Comment: 18 pages, 7 figures