Chunking is a fundamental preprocessing step in retrieval-augmented generation (RAG), yet most existing chunkers rely primarily on heuristics. We introduce the Question--Evidence-Supervised Chunker (QESChunker), to our knowledge the first method for constructing static chunk indices from question--evidence supervision. QESChunker constructs document-specific chunk indices by optimizing over human-annotated or LLM-generated question--evidence pairs, without access to held-out test queries. We formulate non-overlapping and overlapping index construction through a unified question--evidence utility-maximization objective, turning chunking into a supervised combinatorial optimization problem. Under the non-overlap constraint, the objective decomposes over chunks and can be optimized exactly in polynomial time by dynamic programming. When overlap is allowed, the objective becomes monotone submodular; exact optimization is NP-hard, but our greedy achieves a $(1-1/\sqrt{e})$-approximation. Across two self-constructed and three public datasets, both variants outperform existing chunking methods in complete-evidence recall in nearly all evaluated settings, under the same overlap regime and a fixed hybrid retriever. These results recast chunking as supervised, budget-aware index construction for evidence retrieval.

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