Pat the chicken dry and season all over with the salt, cumin, oregano and pepper. Heat the olive oil in a wide Dutch oven over medium-high heat. Brown the thighs skin side down 6 to 7 minutes until deep gold, flip for 2 minutes, then set aside.
Lower the heat to medium. Add the onion and both peppers to the drippings and cook 6 minutes until soft. Stir in the garlic and cilantro for 1 minute.
Add the tomato paste, annatto, turmeric, cumin and oregano. Cook 2 minutes, stirring, until the paste darkens and smells sweet.
Stir in the rinsed brown rice until every grain is coated and golden. Pour in the hot broth, add the bay leaf and salt, and bring to a boil.
Nestle the chicken thighs skin side up on top of the rice. Cover tightly, reduce the heat to low and simmer 45 minutes without stirring, until the rice is tender and the liquid is absorbed.
Scatter the peas and olives over the rice, drizzle in the olive brine, cover and let it rest off the heat 10 minutes. Remove the bay leaf, fluff the rice around the chicken and serve with cilantro and lime.