In a medium bowl, whisk together honey, lime juice, chili powder, cumin, salt, and pepper. Coat the chicken breasts, cover, and refrigerate for at least 30 minutes.

Rinse the rice under cold water and cook according to package instructions, usually boiling, adding salt, and simmering for 18–20 minutes.

Preheat grill or skillet. Cook marinated chicken for 6–7 minutes on each side until internal temperature reaches 165°F. Let rest before slicing.

In a large bowl, combine cooked rice, avocado, cilantro, and sour cream, folding together until creamy and well mixed.

Layer the avocado rice on a plate, top with sliced chicken, and drizzle additional lime juice over the top before serving.