This paper presents a framework for research infrastructures enabling ethically sensitive and legally compliant data science in Europe. Our goal is to describe how to design and implement an open platform for big data social science, including, in particular, personal data. To this end, we discuss a number of infrastructural, organizational and methodological principles to be developed for a concrete implementation. These include not only systematically tools and methodologies that effectively enable both the empirical evaluation of the privacy risk and data transformations by using privacy-preserving approaches, but also the development of training materials (a massive open online course) and organizational instruments based on legal and ethical principles. This paper provides, by way of example, the implementation that was adopted within the context of the SoBigData Research Infrastructure.