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Preheat oven to 450°F with rack in middle. Oil a large 4-sided sheet pan.
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Pulse chips, 2 tsp chili powder, cumin, and 1/4 tsp salt in a food processor until coarsely ground, then transfer to a shallow dish.
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Whisk egg and remaining 2 tsp chili powder in a bowl.
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Season chicken with 1/2 tsp salt. Dip drumsticks in egg, letting excess drip off, then coat with crumbs, pressing to help them adhere. Transfer to sheet pan.
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Bake, without turning, until cooked through, 40 to 45 minutes. Let stand, uncovered, 5 minutes.