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Preheat oven to 450 degrees, with racks in upper and lower thirds.
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On two rimmed baking sheets, arrange chicken, fennel, shallots, and sage.
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In a small bowl, whisk together oil and vinegar and drizzle over chicken and vegetables.
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Toss to combine and season with salt and pepper.
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Roast 35 minutes, rotating sheets halfway through.
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Add apples to sheets and roast until fennel is browned and chicken is cooked through, 15 to 20 minutes more.