In a medium bowl, whisk together honey, lime juice, soy sauce, minced garlic, grated ginger, salt, and pepper until well combined. Add the chicken breasts, ensuring they are coated in the marinade. Cover with plastic wrap and refrigerate for at least 20 minutes, or overnight for deeper flavor.

While the chicken marinates, rinse the rice under cold water until the water runs clear. In a saucepan, combine the rinsed rice, water, and a pinch of salt. Bring to a boil over medium-high heat, reduce heat to low, cover, and simmer for 18 minutes until tender.

Once the rice has rested, fluff it with a fork. Stir in diced avocado, chopped cilantro, and finely chopped red onion. Drizzle lime juice over the mixture and gently toss to combine.

Heat a large skillet over medium heat and add the marinated chicken with half of the marinade. Cook for 7-10 minutes, turning occasionally until browned and cooked through, reaching an internal temperature of 165°F (75°C). Let it rest before slicing.

To assemble, spoon a layer of the avocado rice mixture onto a plate, top with sliced chicken, and garnish with cilantro and lime wedges.