Collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism and lack of complete information. This paper aims to propose a collision avoidance framework that accounts for both measurement uncertainty and bounded motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of possible control actions that are probabilistically safe. The framework entails minimally modifying an existing unconstrained controller to determine a safe controller via a quadratic program constrained to the chance-constrained safety set. The key advantage of the approach is that no assumptions about the form of uncertainty are required other than finite support, also enabling worst-case guarantees. We demonstrate effectiveness of the approach through experiments on a realistic simulation environment.