Preparation 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. Mix remaining 2 teaspoons salt, paprika, and pepper in small bowl. 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. 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.
Preparation 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. Mix remaining 2 teaspoons salt, paprika, and pepper in small bowl. 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. 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.