Most state-of-the-art algorithms for the Vehicle Routing Problem, such as Branch-and- Price algorithms or meta heuristics, rely on a fast feasibility test for a given route. We devise the first approach to approximately check feasibility in the Stochastic Vehicle Routing Problem with time windows, where travel times are correlated and depend on the time of the day. Assuming jointly normally distributed travel times, we use a chance constraint approach to model feasibility, where two different application scenarios are considered, depending on whether missing a customer makes the rest of the route infeasible or not. In addition, we present an adaptive sampling algorithm that is tailored for our setting and is much faster than standard sampling techniques. We use a case study for both scenarios, based on realistic instances, to illustrate that taking correlations and time dependencies into account signicantly improves the quality of the solutions, i.e., the precision of the feasibility decision. In particular, the nonconsideration of correlations often leads to solutions containing infeasible routes.