1. In a small saucepan, heat oil over medium. Add jalapeno, ginger, and garlic. Season with salt and pepper and cook, stirring, until garlic is golden, 2 to 3 minutes. Add sugar and vinegar and cook until sauce is slightly thickened, about 6 minutes. Refrigerate until cool, at least 15 minutes (or up to 1 week).
2. Combine chicken, noodles, cucumber, and cilantro. Drizzle with dressing just before serving.
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