In a large bowl, whisk together olive oil, lemon juice, garlic, oregano, paprika, salt, and pepper
Add chicken pieces and toss to coat evenly
Cover and refrigerate to marinate for at least 1 hour
Thread marinated chicken onto skewers
Preheat grill or grill pan to medium-high heat
Grill chicken skewers until cooked through and slightly charred
Remove from heat and sprinkle with fresh parsley
In a food processor, blend feta, Greek yogurt, olive oil, lemon juice, garlic, and dill until smooth
Transfer dip to a serving bowl
Arrange grilled chicken, warm pita, vegetables, olives, and feta dip on a large serving board
Garnish with parsley and lemon wedges