Modern healthcare has a sharp focus on data aggregation and processing technologies. Consequently, from a data perspective, a patient may be regarded as a timestamped list of medical conditions and their corresponding corrective interventions. Technologies to securely aggregate and access data for individual patients in the quest for precision medicine have led to the adoption of Digital Twins in healthcare. Digital Twins are used in manufacturing and engineering to produce digital models of physical objects that capture the essence of device operation to enable and drive optimization. Thus, a patient’s Digital Twin can significantly improve health data sharing. However, creating the Digital Twin from multiple data sources, such as the patient’s electronic medical records (EMR) and personal health records (PHR) from wearable devices, presents some risks to the security of the model and the patient. The constituent data for the Digital Twin should be accessible only with permission from relevant entities and thus requires authentication, privacy, and provable provenance. This paper proposes a blockchain-secure patient Digital Twin that relies on smart contracts to automate the updating and communication processes that maintain the Digital Twin. The smart contracts govern the response the Digital Twin provides when queried, based on policies created for each patient. We highlight four research points: access control, interaction, privacy, and security of the Digital Twin and we evaluate the Digital Twin in terms of latency in the network, smart contract execution times, and data storage costs.