1. Preheat grill to high. Toss sliced zucchini and fennel in 1 Tbsp. olive oil and season with salt and pepper. Grill (in batches, if necessary) until just tender, 2 to 3 minutes per side for zucchini, 3 to 4 minutes per side for fennel. Remove from grill and let cool slightly. Cut crosswise into 1/2-inch pieces.
2. Remove skin from chicken, pull meat from bones and shred meat. In a large bowl, mix chicken with salad greens and grilled vegetables. Toss in tomatoes, olives, mozzarella and basil.
3. In another bowl, mix vinegar, sugar and 1/4 tsp. each salt and pepper. Stir to dissolve sugar. Add remaining 3 Tbsp. olive oil, whisking to combine. Drizzle vinaigrette over salad, toss and serve.