Mix olive oil with spices and lime juice. Rub on chicken and marinate 15-60 minutes.
Cook rice in water or broth until tender, about 15-20 minutes for white rice. Stir in lime juice.
Grill chicken 6-7 minutes per side until 165°F internal temperature. Rest before slicing.
Cook corn with butter until charred. Mix in mayo, cheese, lime juice, and seasonings.
Whisk sour cream, mayo, lime juice, and spices until smooth.
Layer rice, chicken, corn mixture. Top with dressing and garnish with cilantro and lime.