Prep. Shake the can of coconut milk well, then open and give it a quick stir to combine. Pat the chicken breasts dry with paper towels and set aside.
Make the seasoning. In a small mixing bowl, combine cumin, paprika, oregano, cayenne pepper, salt, and black pepper; stir until thoroughly incorporated.
Cook. Heat 2 tablespoons olive oil in a large skillet over medium heat. Rub the seasoning mixture all over the chicken breasts, then add the chicken to the heated oil and cook for 6 to 7 minutes on each side or until browned and almost cooked through. Cooking time will depend on the size of the chicken breasts. Remove chicken from the skillet and set aside on a plate; keep covered.
Sauté. Add remaining olive oil to the skillet; add onions to the heated oil and cook for 2 to 3 minutes, or until tender and translucent. Stir in garlic and cook for 20 seconds. Add a tablespoon of tomato paste and stir until well combined. Then stir in the tomatoes and continue to cook for 5 minutes, or until the tomatoes are soft.
Cook down the coconut milk and combine. Stir in the coconut milk and bring to a simmer; let simmer for 5 minutes, or until the sauce thickens. Return the chicken breasts to the skillet, reduce heat to medium-low, and cook for 4 to 5 more minutes, or until the chicken is cooked through. The chicken is done when its internal temperature registers at 165˚F.
Taste and adjust before serving. Taste the sauce for salt and pepper; adjust accordingly. Garnish your coconut milk chicken with cilantro or parsley, and serve with lime wedges.