In this paper we present the first neural-based machine translation system trained to translate between standard national varieties of the same language. We take the pair Brazilian - European Portuguese as an example and compare the performance of this method to a phrase-based statistical machine translation system. We report a performance improvement of 0.9 BLEU points in translating from European to Brazilian Portuguese and 0.2 BLEU points when translating in the opposite direction. We also carried out a human evaluation experiment with native speakers of Brazilian Portuguese which indicates that humans prefer the output produced by the neural-based system in comparison to the statistical system.