Chance-constrained stochastic programs (CCSPs) require solutions that satisfy uncertain constraints with high probability. Standard approaches either embed scenarios directly into optimization by considering sample average approximation (SAA)-based reformulations, growing prohibitively expensive and often failing to find feasible solutions; or employ conservative reformulations that guarantee feasibility but sacrifice objective quality by design. We propose ACCESS (Adaptive Chance-Constrained Exploration via Structured Sampling), a structured sampling framework that decouples optimization from feasibility evaluation. First, high-quality candidate solutions are generated by solving many inexpensive single-scenario subproblems, avoiding sampling directly in the constrained high-dimensional solution space. Second, feasibility is assessed separately via large-scale batched simulation over a massive number of scenarios, which is naturally amenable to GPU parallelism. That reduces the search from a high-dimensional solution space to a two-dimensional parameter space controlling conservatism and scenario diversity; while concentrating on candidates near the feasibility boundary, where high-quality feasible solutions lie. We also introduce a variant, ACCESS($δ$), which provides certified feasibility guarantees with probability $1-δ$. Experiments across three benchmark classes and five scenario distributions show that ACCESS matches or exceeds the best objective found by any method in nearly every setting, while ACCESS($δ$) is empirically feasible on every instance. The conservative reformulations remain several percent worse in objective, and SAA is frequently infeasible while taking an order of magnitude longer on the harder benchmarks.

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