The Swiss German dialect corpus ArchiMob poses great challenges for NLP and corpus linguistic research due to the massive amount of variation found in the transcriptions: dialectal variation is combined with intra-speaker variation and with transcriber inconsistencies. This variation is reduced through the addition of a normalisation layer. In this paper, we propose to use character-level machine translation to learn the normalisation process. We show that a character-level machine translation system trained on pairs of segments (not pairs of words) and including multiple language models is able to achieve up to 90.46% of word normalisation accuracy, an error reduction of 45% over a strong baseline and of 34% over a heterogeneous system proposed by Samardzic et al. (2015).