The Internet of Things (IoT) adoption grows significantly and is successful in many different domains. Nevertheless, the ever-growing demand for more connected devices pushes the requirement for scalable IoT architectures capable of maintaining the security and privacy of collected data. The latter is a particularly critical aspect when considering sensitive data, e.g., medical records. One solution to address this challenge is to modify the centralized back-end model to one based on a Blockchain, changing the way IoT data is stored and shared by providing a decentralized peer-to-peer network. This technology enables naming and tracking for connected devices, and in the case of this article, features a high availability of Personal Health Records, yet protecting patients' privacy through the use of cryptography. Furthermore, the addition of Fog computing mechanisms helps to achieve real-time data processing, supports precision medicine, and avoids single points of failure. As a result, devices have a local and more resilient ecosystem for operation. In this context, this work proposes an architecture model named FogChain, which combines the technologies Blockchain, Fog computing, and the IoT for the healthcare domain. Our main contribution is the FogChain model itself, and its concept of overcoming IoT constraints by employing a differential approach, adding an intermediary Fog layer near to the edge to improve their capabilities and resources. Experiments demonstrate that FogChain can achieve a 62.6% faster response time when compared to Cloudlike Blockchain infrastructures. The results obtained from the evaluation endorses the capacity of our model in achieving its goals while retaining application performance.