If using wooden skewers, soak them in water for 20-30 minutes before using.
Line a rimmed baking sheet with aluminum foil; coat lightly with nonstick cooking spray. Adjust one of the oven racks to the top position (about 6 inches from the broiler). Preheat the broiler on HIGH.
In a large measuring cup or jar, combine the olive oil, lemon zest, lemon juice, vinegar, garlic, brown sugar, oregano, parsley, Dijon, salt, and pepper.
Place the chicken in a large bowl or Ziploc bag. Pour about ¾ of the sauce over the chicken; toss to coat. Reserve a little bit of the sauce for brushing or for serving.
Thread the chicken onto the skewers, or let the excess sauce drip off and just add the chicken directly to the sheet pan.
Place under the broiler for 11-14 minutes, or until the chicken is golden brown and reaches an internal temperature of 165°F. Flip the chicken halfway through for even cooking.
Brush the cooked chicken with reserved sauce. Serve with tzatziki sauce and pita bread, rice, and other optional toppings of choice.