The conductivity sigma of amorphous In2O3-x depends sensitively on the oxygen concentration; sigma increases with lower oxygen concentration (increasing x) and reversibly decreases as oxygen is added. Illumination with ultraviolet light releases oxygen and exposure to air reoxidizes causing sigma vary by many orders of magnitude. At a sufficiently large value of x, the material undergoes an insulator-metal transition. We measured the spectrum of conductance fluctuations in thin films of amorphous In2O3-x as a function of oxygen concentration. Between 5 Hz and 10 kHz, the spectra fit well to a 1/f(alpha) power law. For small x, the magnitude of the noise is unusually large, and alpha is near 1.0. As oxygen is removed the noise at first increases and then decreases by a factor of 500 as the material enters the metallic state. At the point where the noise begins to decrease, alpha jumps to about 1.12.