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1
Whisk juices, olive oil, oregano, 1 teaspoon salt, rosemary, and garlic in glass baking dish. Add chicken to marinade. Turn to coat; chill 2 hours, turning occasionally. DO AHEAD: Can be made 1 day ahead. Keep chilled.
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2
Mix remaining 2 teaspoons salt, paprika, and pepper in small bowl.
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3
Spray grill rack with nonstick spray. Prepare barbecue (medium heat). Slice 1/2 orange into 1/4- to 1/8-inch-thick slices. Remove chicken from marinade; pat dry. Loosen skin from chicken breast and slide 1 to 2 orange slices between skin and breast. Loosen skin from thighs and slide 1 to 2 orange slices between skin and thighs. Rub paprika mixture over both sides of chicken. Place chicken, skin side down, on grill. Place foil-wrapped bricks or cast-iron skillet atop chicken (if using bricks, position 1 brick over top half of chicken and 1 brick over bottom half). Cover and grill until skin is crispy and brown, about 15 minutes. Remove bricks or skillet. Using tongs or 2 large spatulas, turn chicken. Replace bricks or skillet and cook, covered, until chicken is cooked through, about 20 minutes longer. Let chicken rest 10 minutes.
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4
Meanwhile, place whole orange on grill and cook until slightly charred, turning often, about 1 minute. Cut into wedges and serve alongside for squeezing over chicken.
