Wash chicken pieces and pat dry with paper towels. Drizzle chicken pieces with 1 tablespoon olive oil and sprinkle with paprika, garlic powder and oregano.
Heat remaining 3 tablespoons oil in a Dutch oven or heavy pan over medium-high heat. Add chicken pieces, four pieces at a time and cook, turning once, until browned on both sides, about 5 minutes. Transfer to a plate and set aside.
Using the same pan, add onion and mushrooms and cook until soft, stirring occasionally. Stir in tomatoes and then add rice and stir constantly for a minute.
Add chicken broth, saffron and browned chicken pieces (plus accumulated juices). Season with salt and pepper. Stir to mix ingredients. Bring to a boil, reduce heat to medium, cover and simmer until the chicken is tender and rice has absorbed the liquid, about 25-30 minutes.