Make the Lemon Vinaigrette: Whisk the lemon juice, white wine vinegar, sugar and oregano in a bowl. Slowly whisk in olive oil. Season with salt and pepper.

Pour 1/4 cup vinaigrette into a large resealable plastic bag. Add chicken; seal bag and turn to coat. Refrigerate for at least 1 hour, turning occasionally.

Grease grill grate. Heat grill to medium.

Pour 1/4 cup vinaigrette into another large resealable plastic bag. Add vegetables; seal bag and toss to coat. Transfer vegetables to a lightly greased grill grid. Season with salt and pepper. Discard bag with vinaigrette.

Remove chicken from marinade; pat dry with paper towels. Discard marinade.

Grill chicken and vegetables, covered, over medium heat for 10-12 minutes or until a thermometer inserted into the chicken reads 165 F and vegetables are crisp-tender, turning once. Remove from the grill. Tent chicken with aluminum foil. Let rest for 10 minutes. Keep vegetables warm.

Brush feta with 2 tablespoons vinaigrette. Grill feta, covered, for 1-2 minutes on each side or until cheese begins to soften. Transfer feta and chicken to a cutting board. Cut feta in half. Thinly slice chicken.

Arrange the chicken, feta and vegetables on a large serving platter. Add olives and capers. Drizzle with remaining vinaigrette. Garnish with oregano.