In this article, we propose a chance-constrained cooperative distributed model predictive control scheme for reference tracking. We consider dynamically coupled linear time-invariant systems that are subject to local and coupling chance constraints. The proposed controller is based on the distributed alternating direction method of multipliers and is able to steer the system to any admissible setpoint while ensuring recursive feasibility under inexact dual optimization and unbounded additive disturbances. Under a central convex unimodality assumption, the chance constraints are guaranteed to hold in closed loop. This article closes with two numerical examples. The first one is of an academic nature in order to highlight the chance constraint satisfaction, convergence, and numerical properties of the proposed algorithm. The second one is a practical scenario of a benchmark process.