Thinly slice zucchini using a vegetable peeler or a mandolin. Lightly toss in some olive oil then spread out on a baking sheet and bake at 350°F until soft, about 10 minutes (or can use an indoor grill). Set aside.
Dressing: whisk together and set aside.
To serve: in a large bowl add grilled zucchini, artichokes, chicken and tomatoes. Drizzle dressing over and toss gently. Sprinkle over cheese and basil, and serve.