The advantages of neural machine translation (NMT) have been extensively validated for offline translation of several language pairs for different domains of spoken and written language. However, research on interactive learning of NMT by adaptation to human post-edits has so far been confined to simulation experiments. We present the first user study on online adaptation of NMT to user post-edits in the domain of patent translation. Our study involves 29 human subjects (translation students) whose post-editing effort and translation quality were measured on about 4,500 interactions of a human post-editor and a machine translation system integrating an online adaptive learning algorithm. Our experimental results show a significant reduction of human post-editing effort due to online adaptation in NMT according to several evaluation metrics, including hTER, hBLEU, and KSMR. Furthermore, we found significant improvements in BLEU/TER between NMT outputs and professional translations in granted patents, providing further evidence for the advantages of online adaptive NMT in an interactive setup.