We present a self-organizing Kohonen neural network for quantizing colour graphics images. The network is compared with existing algorithmic methods for colour quantization. It is shown experimentally that, by adjusting a quality factor, the network can produce images of much greater quality with longer running times, or slightly better quality with shorter running times than the existing methods. This confounds the frequent observation that Kohonen neural networks are necessarily slow. The continuity of the colour map produced can be exploited for further image compression, or for colour palette editing.