Digital technologies carry the promise of transforming science and opening up the research process. We interviewed researchers from a variety of backgrounds about their attitudes towards and experiences with openness in their research practices. We observe a considerable discrepancy between the concept of open science and scholarly reality. While many researchers support open science in theory, the individual researcher is confronted with various difficulties when putting open science into practice. We analyse the major obstacles to open science and group them into two main categories: individual obstacles and systemic obstacles. We argue that the phenomenon of open science can be seen through the prism of a social dilemma: what is in the collective best interest of the scientific community is not necessarily in the best interest of the individual scientist. We discuss the possibilities of transferring theoretical solutions to social dilemma problems to the realm of open science.