Robots have potential to revolutionize the way we interact with the world around us. One of their greatest potentials is in the domain of mobile health, where they can be used to facilitate clinical interventions. However, to accomplish this, robots need to have access to our private data in order to learn from these data and improve their interaction capabilities. To enhance this learning process, knowledge sharing among multiple robot units is the natural step forward. However, to date, there is no well-established framework which allows for such data sharing while preserving the privacy of the users, such as hospital patients. To this end, we introduce RoboChain: the first learning framework for secure, decentralized, computationally efficient data and model sharing among multiple robot units installed at multiple sites such as hospitals. RoboChain builds upon and combines the latest advances in open data access, blockchain technologies, and machine learning. We illustrate this framework using the example of a clinical intervention conducted in a private network of hospitals. Specifically, we lay down the system architecture that allows multiple robot units, conducting the interventions at different hospitals, to perform efficient learning without compromising the data privacy.