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1
Zest 2 large or 3 medium oranges and set oranges aside. In a food processor, whirl zest, lemongrass, 2 1/2 tsp. sugar, the salt, and chile flakes until very finely minced, scraping inside of container several times. Set aside 1 tbsp. In a medium bowl, turn chicken in 1 tbsp. oil to coat. Pat evenly all over with remaining lemongrass mixture. Chill, covered, at least 2 hours.
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2
Meanwhile, in a small saucepan over medium heat, cook shallots in remaining oil (about 2 cups), stirring often, until deep golden brown, 30 to 35 minutes. With a slotted spoon, transfer shallots to paper towels to drain and crisp. Set oil aside.
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3
While shallots cook, cut peel (including all white pith on outside of fruit) from unzested oranges, following curve of fruit. Working over a bowl, cut between inner membranes to free segments. Squeeze juice from membranes into bowl. Tip juice into a measuring cup; if needed, squeeze zested oranges to make about 6 tbsp. juice. Return juice to segments; set aside. Preheat oven to 450u00b0.
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4
Heat a 12-in. ovenproof frying pan over medium-high heat. Swirl 1 tbsp. shallot oil in pan and brown chicken, skin side down, 4 to 7 minutes. Remove from heat and turn chicken over. Roast chicken in oven until no longer pink in center (cut to test), 12 to 16 minutes.
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5
Meanwhile, add lime juice, fish sauce, 1 1/2 tbsp. shallot oil, reserved 1 tbsp. lemongrass mixture, and remaining 1 1/2 tsp. sugar to oranges. (Save remaining oil for other uses.) Slice cucumber into 1/4-in. rounds. Cut slices in half, then into small triangles.
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6
Set chicken on plates. With a slotted spoon, lift oranges in bowl from dressing and arrange over chicken. Scatter cucumber, half of shallots, and the cilantro on top. Pour dressing into a pitcher. Serve chicken immediately, with dressing and more shallots on the side.
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7
Make ahead: Through step 2, up to 1 day, shallots stored airtight.
