Leveraging the power of a graph neural network (GNN) with message passing, we present a Monte Carlo Tree Search (MCTS) method to solve stochastic orienteering problems with chance constraints. While adhering to an assigned travel budget the algorithm seeks to maximize collected reward while incurring stochastic travel costs. In this context, the acceptable probability of exceeding the assigned budget is expressed as a chance constraint. Our MCTS solution is an online and anytime algorithm alternating planning and execution that determines the next vertex to visit by continuously monitoring the remaining travel budget. The novelty of our work is that the rollout phase in the MCTS framework is implemented using a message passing GNN, predicting both the utility and failure probability of each available action. This allows to enormously expedite the search process. Our experimental evaluation shows that with the proposed method and architecture we manage to efficiently solve complex problem instances while incurring in moderate losses in terms of collected reward. Moreover, we demonstrate how the approach is capable of generalizing beyond the characteristics of the training dataset. The paper's website, open-source code, and supplementary documentation can be found at ucmercedrobotics.github.io/gnn-sop.