In a large zip-top bag, combine the chicken with lemon juice, white wine vinegar, oregano, garlic powder, thyme, salt, and pepper.
Seal the bag and massage the marinade into the chicken.
Refrigerate for at least 30 minutes or up to 8 hours.
Remove the chicken from the marinade and discard the remaining marinade.
Pat the chicken lightly with paper towels.
Heat olive oil in a large skillet over medium heat.
Cook the chicken for 4–5 minutes per side until golden and the internal temperature reaches 165°F (74°C).
Let the chicken rest for 8–10 minutes before slicing into strips.
In a large bowl, combine cucumber, tomatoes, olives, red onion, feta, olive oil, vinegar, oregano, garlic powder, dill, salt, and pepper.
Stir until evenly combined.
Assemble the Greek Chicken Bowls by adding cooked rice, sliced chicken, and the cucumber salad to serving bowls.
Garnish with extra feta if desired and serve immediately.