Combine the first 4 ingredients in a small bowl. Sprinkle chicken with the oregano mixture.
Heat Annatto Oil in a large nonstick skillet over medium-high heat. Add the chicken; cook 8 minutes, turning once. Reduce heat to medium. Add Sofrito and tomato; cook 3 minutes, stirring frequently. Add rice, wine, ham, and alcaparrado; cook 1 minute, stirring constantly. Add the water and chicken broth; bring to a boil. Cover, reduce heat, and simmer for 20 minutes. Stir in the peas, and cook for 5 minutes or until the rice is tender.
Alcaparrado is a mixture of whole green olives, pimentos, and capers; look for it in the Latin section of the supermarket or in Latino markets. Be sure to let your guests know that the olives from the bottled mixture aren't pitted.