Although considerable progress has been made in determining the cognitive architecture of spelling, less is known about the serial-order mechanism of spelling: the process(es) involved in producing each letter in the proper order. In this study, we investigate compound chaining as a theory of the serial-order mechanism of spelling. Chaining theories posit that the retrieval from memory of each element in a sequence is dependent upon the retrieval of previous elements. We examine this issue by comparing the performance of simple recurrent networks (a class of neural networks that we show can operate by chaining) with that of two individuals with acquired dysgraphia affecting the serial-order mechanism of spelling-the graphemic buffer. We compare their performance in terms of the effects of serial position, the effect of length on overall letter accuracy, and the effect of length on the accuracy of specific positions within the word. We find that the networks produce significantly different patterns of performance from those of the dysgraphics, indicating that compound chaining is not an appropriate theory of the serial-order mechanism of spelling.