Recent work on intracranial brain-machine interfaces has demonstrated that spoken speech can be decoded with high accuracy, essentially by treating the problem as an instance of supervised learning and training deep neural networks to map from neural activity to text. However, such networks pay for their expressiveness with very large numbers of labeled data, a requirement that is particularly burdensome for invasive neural recordings acquired from human patients. On the other hand, these patients typically produce speech outside of the experimental blocks used for training decoders. Making use of such data, and data from other patients, to improve decoding would ease the burden of data collection -- especially onerous for dys- and anarthric patients. Here we demonstrate that this is possible, by reengineering wav2vec -- a simple, self-supervised, fully convolutional model that learns latent representations of audio using a noise-contrastive loss -- for electrocorticographic (ECoG) data. We train this model on unlabelled ECoG recordings, and subsequently use it to transform ECoG from labeled speech sessions into wav2vec's representation space, before finally training a supervised encoder-decoder to map these representations to text. We experiment with various numbers of labeled blocks; for almost all choices, the new representations yield superior decoding performance to the original ECoG data, and in no cases do they yield worse. Performance can also be improved in some cases by pretraining wav2vec on another patient's data. In the best cases, wav2vec's representations decrease word error rates over the original data by upwards of 50%.