Cook the brown rice according to package instructions, then set aside.
Prepare the cucumber-tomato-kalamata salad by combining the peeled chopped cucumber, chopped tomato, 1/2 cup sliced kalamata olives, 1/4 cup finely chopped red onion, 2 Tbsp avocado oil, zest of 1 lemon, 1 Tbsp lemon juice, and 1 small minced garlic clove; toss and season to taste.
Make the chicken marinade: whisk together 1/4 cup avocado oil, 2 Tbsp fresh lemon juice, 2 tsp lemon zest, 2 Tbsp finely chopped red onion, 4 minced garlic cloves, 2 Tbsp chopped fresh parsley, 1 tsp dried oregano, 1 tsp dried thyme, and 1/2 tsp sea salt.
Place the chicken pieces in a large zip-top bag or shallow dish and pour in the marinade; seal or cover and coat the chicken evenly. Marinate at least 20 minutes, or up to 24 hours in the refrigerator.
Preheat the oven to 350°F (175°C). Transfer the marinated chicken and any excess marinade to a single layer in a baking dish or rimmed baking sheet.
Bake the chicken until it reaches an internal temperature of 165°F (74°C): about 20–25 minutes for thin cutlets or 25–35 minutes for thicker breasts. Use a meat thermometer inserted into the thickest part for accuracy.
Remove the chicken from the oven and let it rest for 15 minutes, then slice or chop into strips or cubes.
Assemble bowls: divide cooked rice among 4 bowls, top with sliced garlic-herb chicken, the cucumber-tomato-kalamata salad, hummus, and crumbled feta as desired.