In a large bowl or resealable plastic bag combine the olive oil, minced garlic, lemon juice, and red pepper flakes. Add the strips of chicken and toss until all the pieces are evenly coated in the mixture. Marinate for 30 minutes or overnight for more flavor.
In a large bowl, mix together the softened butter, minced garlic, lemon zest and juice, Dijon mustard, paprika, red pepper flakes, chives, salt, and black pepper until well combined. Reserve some of the butter mixture to brush on the chicken skewers after they are cooked. Set aside.
Thread the chicken onto the skewers evenly. Don’t crowd them.
Preheat a grill to medium-high heat. Place the chicken skewers on the grill and cook for 4-5 minutes on each side, basting with the butter sauce as it cooks. The chicken should reach an internal temperature of 165°F/75°C.
Once cooked, remove the skewers. Brush with reserved cowboy butter and sprinkle with fresh parsley.