Advances in computer science have raised concerns about the privacy of personal information. Therefore solutions to address these concerns have to be found. Blockchain enables new approaches to solve privacy issues in distributed systems, but at the same time also raises new concerns with its openness and immutability. The European Union has taken steps towards addressing information privacy concerns and define rights of data subjects and obligations of controllers and processors of personal data. We will apply and discuss these in light of current Blockchain implementations. This will result in a guideline for GDPR compliant Blockchain developments in the future.