1. Adjust oven rack to middle position and heat oven to 350°F. Place garlic and 1 teaspoon salt in large bowl; using rubber spatula, mix to make smooth paste. Add oregano, 1 tablespoon vinegar, and 1/2 teaspoon black pepper to garlic-salt mixture; stir to combine. Place chicken in bowl with marinade. Coat chicken pieces evenly with marinade; set aside for 15 minutes.

2. Heat 1 tablespoon oil in Dutch oven over medium heat until shimmering. Add onion, green pepper, and pepper flakes; cook, stirring occasionally, until vegetables begin to soften, 4 to 8 minutes. Add 2 tablespoons cilantro; stir to combine. Push vegetables to sides of pot and increase heat to medium-high. Add chicken to clearing in center of pot, skin side down, in even layer. Cook, without moving chicken, until outer layer of meat becomes opaque, 2 to 4 minutes. (If chicken begins to brown, reduce heat to medium.) Using tongs, flip chicken and cook on second side until opaque, 2 to 4 minutes more. Add tomato sauce, broth, and water; stir to combine. Bring to simmer; cover, reduce heat to medium-low, and simmer until chicken registers 160°F on instant-read thermometer, about 20 minutes. Using tongs, transfer chicken to large plate, wrap tightly with foil, and set aside.

3. Add rice, olives, capers, and 3/4 teaspoon salt; stir well. Bring to simmer, cover, and place pot in oven. After 10 minutes, remove pot from oven and gently stir rice once from bottom up. Return pot to oven. After another 10 minutes, stir once more, adding 1/4 cup water if rice appears dry and bottom of pot is beginning to burn. Cover and return pot to oven; cook until rice has absorbed all liquid and is tender but still holds its shape, about 10 minutes longer.

4. Remove and discard skin from chicken. Using 2 spoons, pull meat off bones in large chunks. Place chicken, along with any accumulated juices, in large bowl and toss with remaining tablespoon olive oil, remaining 2 teaspoons vinegar, remaining 2 tablespoons cilantro, and pimentos; season with salt and pepper to taste. Place chicken on top of rice, cover, and let stand until warmed through, about 5 minutes. Serve, passing lemon wedges separately.

Serves 4 to 6