Remove skin from chicken. Remove all fat from skin (should have only thin layer of skin remaining.) Place in small bowl or ziploc bag and add salt, pepper, cayenne, sugar. Rub mix all over skin. Refrigerate for at least one hour. Blot dry with paper towel. Fry in oil at 370 degrees until golden brown. Break into shards.
While chicken skin is refrigerating:
Saute onion and garlic in butter over medium heat until lightly caramelized. Add diced squash to onions. Reduce heat to low and simmer until squash in fully tender (about 30 mins.). Add cream to squash mixture. Transfer squash to blender (or hand blend) on high. Season with salt and peppert and lemon juice to taste. Pass through chinois. Reserve mixture.
Score tomatoes. Blanch them in boiling water and then shock in ice bath.Peel skins. Season with salt and pepper and olive oil.
Spoon squash mixture onto bottom of plate. Top with tomatoes. Sprinkle on chicken skin shards.