Whether you are skinning the chicken or not, rinse it and pat it dry. Season with the salt, pepper, thyme, and oregano.
Heat the oil and butter together in a 12 – 14-inch deep skillet; when hot, add the chicken seasoned side down. Brown both sides, turning once; about 10 minutes total. Remove the chicken to a platter.
Add the onion and garlic to the pan and saute for about 5 minutes; or until getting browned. Add the rice and saute 2 – 3 minutes.
Add the broth, roasted red peppers, saffron, bay leaf and a dash of salt and pepper; stir. Add back the chicken, nestling it into the rice; pour in any accumulated juices from the platter. Cover tightly and simmer for 20 minutes, or until most of the liquid has been absorbed. Take off heat and pour the peas over the top; add the olives; cover and allow to stand 10 minutes more.
Remove the chicken to a warmed serving plate. Stir the peas and olives into the rice and spoon onto the plate. Garnish with chopped parsley, if desired.