Blockchain technologies have generated excitement, yet their potential to enable new forms of governance remains largely unexplored. Two confronting standpoints dominate the emergent debate around blockchain-based governance: discourses characterised by the presence of techno-determinist and market-driven values, which tend to ignore the complexity of social organisation; and critical accounts of such discourses which, whilst contributing to identifying limitations, consider the role of traditional centralised institutions as inherently necessary to enable democratic forms of governance. Therefore the question arises, can we build perspectives of blockchain-based governance that go beyond markets and states? In this article we draw on the Nobel laureate economist Elinor Ostrom’s principles for self-governance of communities to explore the transformative potential of blockchain. We approach blockchain through the identification and conceptualisation of affordances that this technology may provide to communities. For each affordance, we carry out a detailed analysis situating each in the context of Ostrom’s principles, considering both the potentials of algorithmic governance and the importance of incorporating communities’ social practices. The relationships found between these affordances and Ostrom’s principles allow us to provide a perspective focussed on blockchain-based commons governance. By carrying out this analysis, we aim to expand the debate from one dominated by a culture of competition to one that promotes a culture of cooperation.