The cross section for photodetachment of I- at 347 nm, 0.5 eV above threshold, has been determined to be (2.9+/-0.5) × 10-17 cm2. This value has been obtained in a crossed-beam experiment by comparison with photodetachment from H- at 993 nm, 0.5 eV above its threshold. The present determination permits placement of the previously determined relative-cross-section curve for the first electron volt above threshold on an absolute scale. The entire experimental curve is compared with the recent calculation of Robinson and Geltman. Although the shapes of the two curves are very similar, the new experimental cross section exceeds the calculation by nearly a factor of 2.