With the emergence of the Internet of Things, new services in healthcare will be available and existing systems will be integrated in the IoT framework, providing automated medical supervision and efficient medical treatment. Context awareness plays a critical role in realizing the vision of the IoT, providing rich contextual information that can help the system act more efficiently. Since context in healthcare has its unique characteristics, it is necessary to define an appropriate context aware framework for healthcare IoT applications. We identify this context as perceived in healthcare applications and describe the context aware procedures. We also present an architecture that connects the sensors that measure biometric data with the sensory networks of the environment and the various IoT middleware that reside in the geographical area. Finally, we discuss the challenges for the realization of this vision.