Bootstrapping provides a novel approach to training a neural network to estimate the chromaticity of the illuminant in a scene given image data alone. For initial training, the network requires feedback about the accuracy of the network's current results. In the case of a network for color constancy, this feedback is the chromaticity of the incident scene illumination. In the past, prefect feedback has been used, but in the bootstrapping method feedback with a considerable degree of random error can be used to train the network instead. In particular, the grayworld algorithm, which only provides modest color constancy performance, is used to train a neural network which in the end performs better than the grayworld algorithm used to train it.