The pandemic in 2020 and 2021 had enormous economic and societal consequences, and studies show that contact tracing algorithms can be key in the early containment of the virus. While large strides have been made towards more effective contact tracing algorithms, we argue that privacy concerns currently hold deployment back. The essence of a contact tracing algorithm constitutes the communication of a risk score. Yet, it is precisely the communication and release of this score to a user that an adversary can leverage to gauge the private health status of an individual. We pinpoint a realistic attack scenario and propose a contact tracing algorithm with differential privacy guarantees against this attack. The algorithm is tested on the two most widely used agent-based COVID19 simulators and demonstrates superior performance in a wide range of settings. Especially for realistic test scenarios and while releasing each risk score with epsilon=1 differential privacy, we achieve a two to ten-fold reduction in the infection rate of the virus. To the best of our knowledge, this presents the first contact tracing algorithm with differential privacy guarantees when revealing risk scores for COVID19.