The increasing expansion of renewable energy sources leads to the growth of uncertainty in the distribution network operation. Short-term operational planning performed by distribution system operators should evolve to address those new operating conditions, in particular to allow the efficient utilization of different flexibility levers. In this work, the use of a chance-constrained Alternating Current Optimal Power Flow (AC-OPF) is proposed to model the operational planning problem, considering the activation of several levers such as power modulation and power curtailment. The correlation between the renewable generation profiles and loads is considered via a joint probability constraint approximated with scenarios. The main novelty of the present manuscript is the adoption of a Difference-of-Convex approach that allows to solve the obtained optimization problem without convexification or linearization of the core OPF equations. Furthermore, the approach yields a natural and embarrassingly parallelizable scenario decomposition. The method starts with a reformulation of the model as a Difference-of-Convex optimization problem, and then a proximal bundle method algorithm is applied to solve it. The proposed methodology is tested in a 33 bus distribution network with 11 different values for the safety level defining the probability constraint, ranging from 0.75 to 1.