The success of self-attention in NLP has led to recent applications in end-to-end encoder-decoder architectures for speech recognition. Separately, connectionist temporal classification (CTC) has matured as an alignment-free, non-autoregressive approach to sequence transduction, either by itself or in various multitask and decoding frameworks. We propose SAN-CTC, a deep, fully self-attentional network for CTC, and show it is tractable and competitive for end-to-end speech recognition. SAN-CTC trains quickly and outperforms existing CTC models and most encoder-decoder models, with character error rates (CERs) of 4.7% in 1 day on WSJ eval92 and 2.8% in 1 week on LibriSpeech test-clean, with a fixed architecture and one GPU. Similar improvements hold for WERs after LM decoding. We motivate the architecture for speech, evaluate position and downsampling approaches, and explore how label alphabets (character, phoneme, subword) affect attention heads and performance.