Remove the skin from the chicken breast. Slice the chicken breasts off the bone and slice each piece across horizontally to get 4 large, thin pieces.
When the grill is hot, brush the grill grates with cooking oil to prevent the chicken from sticking. Sprinkle the chicken pieces with salt and pepper and grill for 4 minutes per side. Let rest for a few minutes, and then slices into strips, if desired.
In a large bowl, whisk together the olive oil, Italian seasoning, sugar, lemon juice, half the zest and season with a pinch of salt and pepper. (Reserve the remaining half of the lemon zest for another recipe.) Reserve 2 tablespoons of the dressing to drizzle over the top of the salad.
Add the green beans, olives, cheese, onions and lettuce to the remaining dressing, and toss to coat evenly. Divide the salad evenly among 4 plates or 1 large platter and top with the sliced chicken. Drizzle with the reserved dressing.