Mix olive oil, garlic, basil, salt, and pepper in a small bowl. Toss chicken in marinade, cover and refrigerate overnight.
Heat 1 tablespoon of olive oil in a small saucepan over medium-high heat; cook chicken and set aside. Heat remaining 1 tablespoon of olive oil, and cook garlic and onion until translucent. Stir in jalapeno, chopped tomatoes, salt, and turmeric; cook for 2 minutes to soften tomato. Stir in the rice, mixing thoroughly. Stir in half of the lime juice, bay leaves, chicken stock, water, and cooked chicken. Bring to a boil, reduce heat to low, then cover and simmer 25 minutes, stirring occasionally until the rice has cooked. Remove from heat, discard the bay leaves; stir in the remaining lime juice and cilantro.