Grill or boil chicken until done and cut into thin slices. Set aside.
Mince 3 cloves of garlic, and combine in a small bowl with mayonnaise, anchovies, 2 tablespoons of the Parmesan cheese, Worcestershire sauce, mustard, and lemon juice. Season to taste with salt and black pepper. Refrigerate until ready to use.
Place chicken in a large bowl, add dressing, and toss. Then, add remaining ingredients and toss again.