Modern distribution system operators are facing constantly changing operating conditions caused by the increased penetration of intermittent renewable generators and other distributed energy resources. Under these conditions, the distribution system operators are required to operate their networks with increased uncertainty, while ensuring optimal, cost-effective, and secure operation. This paper proposes a centralized scheme for the operational planning of active distribution networks under uncertainty. A multi-period optimal power flow algorithm is used to compute optimal set-points of the controllable distributed energy resources located in the system and ensure its security. Computational tractability of the algorithm and feasibility of the resulting flows are ensured with the use of an iterative power flow method. The system uncertainty, caused by forecasting errors of renewables, is handled through the incorporation of chance constraints, which limit the probability of insecure operation. The resulting operational planning scheme is tested on a low-voltage distribution network model using real forecasting data for the renewable energy sources. We observe that the proposed method prevents insecure operation through efficient use of system controls.