Place the chicken thighs, water, chicken soup base, lime juice, garlic infused oil, salt, cumin, and crushed red pepper in a slow cooker and gently stir. Cover and cook on low 5 hours or on high for 2 1/2 hours.
Stir in the 1 cup rice, cover and continue to cook on low for 1 hour or on high for 1/2 hour, or until rice is tender and liquid is absorbed.
Stir in the cilantro, breaking the chicken up into large pieces. Spread mixture out evenly in the slow cooker and sprinkle evenly with the shredded cheddar cheese. Cover slow cooker again and cook for 5 to 10 minutes, or until cheese is melted.
Serve with sour cream, salsa, and extra chopped cilantro if desired.