Heat oil over medium-high heat. Cook chicken until browned on all sides, 8-10 minutes. Remove and set aside.
Add onion to pot; cook until translucent, 4-5 minutes.
Add sofrito; cook 1-2 minutes.
Add olives, pimentos, and seasonings; cook 3-4 minutes.
Add rice; cook 30 seconds - 1 minute.
Return chicken to pot; stir.
Stir in tomato sauce and 3 cups water. Optionally add annatto powder. Simmer.
Cover, reduce heat to low. Cook until rice is 80% done, 10-12 minutes.
Stir rice, replace the lid, and continue cooking until done. Add water if needed.
Turn off the heat, stir, cover, let rest for 5-10 minutes.
Serve with lime wedges and cilantro.