First, prepare the cilantro-lime chicken. Combine the juice from 2 limes, 1/2 bunch chopped cilantro, avocado oil, and minced garlic in a medium bowl. Then, add the chicken to the bowl and stir until chicken is evenly coated in the marinade. Cover and refrigerate for 30 minutes.
While the chicken marinates, prepare the Cilantro-Lime Crema. Combine the lime juice, chopped cilantro, sour cream, avocado flesh, and sea salt in a blender. Blend on medium speed until smooth, scraping the sides and bottom of the blender with a rubber spatula to ensure all the chunks of avocado break up. Transfer crema to a small bowl, cover, and refrigerate for at least 20 minutes.
Next, cook the Cilantro-Lime Chicken. Preheat a cast iron grill pan over medium-high heat and lightly grease with cooking spray. Transfer marinated chicken to the pan and grill until cooked through, flipping every 3 minutes, about 9-12 minutes total. Then remove the chicken from the grill pan and let rest for 2-3 minutes.
Finally, plate the dishes. Create a bed of brown rice (about a half cup per plate), then top with fresh slices of avocado and chicken. Drizzle with cilantro-lime crema and serve immediately.