This paper is about obtaining stable vehicle platooning by using Cooperative Adaptive Cruise Control when the communication is unreliable and suffers from message losses. We model communication losses as independent random events and we propose an original design for the cooperative controller, which effectively mitigates the effects of the losses. Our design explicitly takes into account the stochastic nature of the losses by considering both the average evolution of the system and the stochastic variations around it. The control design promotes both plant stability and string stability of the average error dynamics by an H ∞ approach, while minimizing the variance of the trajectories around their average. We show by simulations that the proposed controller is able to compensate losses even for high loss probabilities.