Cover Chicken with cold water in a large pot. Bring to a bare simmer and poach for 1 hour.
Remove chicken from pot to a large bowl, and cover with cold water to stop cooking and firm.
Remove skin and bones by hand. Gently separate meat into bite sized pieces. Strain chicken and place in a dry bowl.
Meanwhile, mash Anchovy Fillets and crushed Garlic into Extra Virgin Olive Oil, and stir in Basil ribbons.
While chicken pieces are still slightly warm, add olive oil mixture, and toss with the Lettuce pieces, Tomato wedges,Cucumber and Salami slices.
Top with Shaved Parmigiano Reggiano, spritz with Balsamic Vinegar, and serve.
