Trim the fat and slice large breasts in half widthwise. Pound chicken to even thickness (ensures the best grilling!) Set aside in a large plastic sealable bag. For the marinade: place the cilantro leaves, minced garlic (or 3-4 garlic cloves), 1 teaspoon orange zest, 1/2 cup freshly squeezed orange juice, 1/4 cup freshly squeezed lime juice, dried oregano flakes, cumin powder, 1 teaspoon salt and 1/2 teaspoon pepper, and fresh mint leaves in a food processor. Cover and pulse until cilantro, mint, and garlic is finely chopped. Drizzle in the olive oil and pulse until just combined. Do not blend vigorously with the olive oil. Reserve 1/3 cup of this marinade and set aside.
Pour remaining marinade over chicken. Knead to coat chicken and place in the fridge for at least 1 hour up to 12 hours. The longer the chicken marinades, the more flavorful it will be.
Lightly oil the grill grate and then place the marinated chicken (discard marinade in bag) on the grill. Cook for 10-12 minutes turning as needed (depending on the size of your pieces) or until chicken juices run clear and internal temperature is at 165 degrees F. As you flip and cook the chicken, brush it generously with 1/4 cup of the the reserved marinade. Add the last tablespoon or so of the marinade to finished chicken after removing from the grill. Tent with foil and allow to rest for 5 minutes before slicing/chopping.
Prepare cilantro-lime rice: combine the rice, chicken stock or broth, and minced garlic in a pot over high heat. As soon as the mixture begins to boil, reduce the heat, and cover with a lid until the rice is cooked through. Once the rice is cooked through, tender, and no liquid remains, stir in 3 tablespoons (1 large) lime juice and 3 tablespoons packed & finely chopped cilantro. Season to taste with salt and pepper.
For the salsa: finely chop the red onion and then soak in a bowl or cup of cold water while preparing the rest of the salsa (this will take away the bite). Zest one of the oranges to get 1 teaspoon zest. Peel the cara cara orange and navel or tangelo and then segment the oranges. Dice the segments into small pieces and place in a medium-sized bowl. Add the garlic, orange zest, and finely chopped cilantro. Add the diced avocado and top with 1 teaspoon lime zest and 2 tablespoons lime juice. If desired add in the finely diced jalapeno. Add a generous pinch of salt and freshly cracked pepper. Drain red onion and add. Gently stir to combine.
In separate bowls, layer the cilantro-lime rice, the grilled chicken (slice or chop), and even parts citrus avocado salsa.
Top bowls with fresh lime wedges and fresh cilantro as desired. Enjoy immediately.