Heat olive oil over medium heat in a large skillet. Sprinkle chicken thighs on all sides with liquid smoke if using, salt and pepper and put in the skillet skin side down. Cook, turning, until browned on all sides, about 10 minutes.
Remove chicken thighs to a plate, pour off some of the fat in skillet and return to heat. Add onion, garlic, pepper and sausage; saute 3 minutes or until onion is softened. Stir in rice, oregano, turmeric and saffron; saute 2 minutes. Add broth and tomatoes and bring to a boil. Reduce heat and simmer 15 minutes.
Place chicken thighs in a single layer on top of rice; top with peas. Cover with foil and cook on medium-low 15 minutes or until rice is tender and chicken thighs are cooked through. Stir, season to taste with additional salt and pepper and serve.