Heat vegetable oil in a large saucepan over medium heat. Season chicken pieces with salt and paprika; fry chicken in the hot oil until browned, about 5 minutes per side. Transfer chicken to a plate. Drain excess grease from skillet.
Melt butter in the same skillet over medium heat; stir rice and saffron into hot butter and cook until rice is yellow and slightly fragrant, about 3 minutes. Stir stock into rice and cook until rice is slightly softened, about 10 minutes. Return chicken parts to skillet, stir in red bell pepper, and cover. Simmer about 10 minutes. Gently fold green peas into mixture. Continue to simmer until chicken is tender and no longer pink inside and liquid has been absorbed by rice, 10 to 15 more minutes.