Marinate the chicken for approximately 10 minutes in a bowl containing the green peppers, oregano, garlic, black pepper, olives, celery, parsley, coriander, and thyme.
In an iron pot, heat 3 tablespoons of oil, reserving 2 tablespoons for later use. Add sugar to heated oil and quickly stir. When sugar turns dark brown, add the chicken (without the vegetables), being careful with splattering oil. Stir, cover and let simmer at medium heat for 10 minutes, adding tablespoonfuls of water regularly to prevent it from burning. Add the vegetables. Add tomato paste and stir to combine. Add remaining water and bring to a boil. Add salt to taste.
Add the rice and stir often to avoid excessive sticking. Once all the water has evaporated, cover with a tight-fitting lid and simmer over very low heat. Wait 15 minutes, uncover and stir, before adding remaining oil. Cover and wait another 5 minutes. Taste rice for doneness; it should be firm but tender inside. If necessary, cover and leave another 5 minutes over very low heat.