01 - Combine olive oil, lemon juice, garlic, smoked paprika, cumin, oregano, red pepper flakes, salt, and black pepper in a large bowl. Add chicken breasts and toss to coat evenly. Marinate for at least 15 minutes, up to 2 hours for deeper flavor penetration.
02 - Preheat grill or grill pan over medium-high heat. Grill marinated chicken for 6-7 minutes per side until cooked through and juices run clear. Remove from heat and let rest for 5 minutes before slicing to retain juices.
03 - In a large bowl, combine diced cucumber, halved cherry tomatoes, sliced red onion, olives, and chopped parsley. Drizzle with olive oil and red wine vinegar. Toss gently to combine and season with salt and pepper to taste.
04 - Slice rested chicken against the grain. Arrange over or alongside the cucumber salad. Garnish with fresh lemon wedges and additional parsley if desired. Serve immediately while chicken is still warm.