Preheat oven to 450°. Using kitchen shears, cut out backbone and neck from chicken and press firmly on chicken to flatten. Set chicken, skin side up, on a rimmed baking sheet and brush with 1 tbsp. oil; sprinkle with 3/4 tsp. salt and 1/2 tsp. pepper. Bake until no longer pink in the center, about 30 minutes.
Whisk together 1/4 cup oil, the lemon zest and juice, garlic, sugar, and remaining 1/4 tsp. each salt and pepper in a bowl.
Gently toss remaining ingredients in another bowl to combine.
Quarter chicken. Put salad on plates, top with chicken, and then dressing.
*If your grocery store doesn't sell small chickens, use a larger one and bake longer. Also, you can ask a butcher to remove the backbone and neck, or buy a quartered chicken.