A quick soak in an orange juice brine infuses the chicken with lots of flavor. You’ll need a total of about 9 medium oranges for this recipe.
Combine the orange juice, zest, 6 Tbs. salt, and 4 cups water in a large bowl or pot; stir to dissolve the salt. Add the chicken breasts and refrigerate for 2 to 3 hours.
Position a rack in the center of the oven and heat the oven to 400°F.
Remove the chicken from the brine and pat it dry with paper towels.
Heat the olive oil in a 12-inch oven-proof skillet over medium-high heat until shimmering hot. Add the chicken skin side down in a snug single layer and cook until the skin is golden brown, 3 to 5 minutes. Turn the chicken, season with 1/4 tsp. salt and a few grinds of pepper, and put the pan in the oven. Roast the chicken until an instant-read thermometer registers 165°F in the center of the thickest breast, about 15 minutes. Remove from the oven, transfer the chicken to a carving board, tent with foil, and let rest while you make the sauce.
Pour the juices from the skillet into a heatproof measuring cup. Let the fat rise to the surface and then spoon it off.
Melt 2 Tbs. of the butter in the skillet over medium-high heat. Add the shallot and cook, stirring, until soft, 1 to 2 minutes. Off the heat, add the brandy. Return the pan to the heat and cook, scraping the bottom of the pan, until the brandy has almost evaporated, about 30 seconds. Increase the heat to high and add the orange juice. Boil until thick and syrupy and reduced to about 1/3 cup, about 5 minutes. Add the chicken broth, pan juices, and any juices from the carving board. Boil until reduced to about 3/4 cup, about 3 minutes.
Swirl in the orange segments. Then, off the heat, swirl in the remaining 1 Tbs. butter and the parsley until the butter is melted. Season to taste with salt and a few grinds of pepper.
To serve, cut the chicken on the diagonal into thin slices and arrange on 6 serving plates. Drizzle with the sauce.
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