Season the chicken with salt and pepper. Heat 1 tablespoon of the oil in a medium saute pan over medium-high heat. Add the chicken, and when its underside has turned deep golden brown (after about 1 minute), turn it with a metal spatula. Turn occasionally for even browning until almost cooked through, 3 to 5 minutes. Transfer to a bowl.

Reduce the heat to medium. Heat the remaining 1-1/2 teaspoons oil in the pan and add the garlic, anchovies, and orange zest. Cook until the garlic is golden and the mixture is fragrant, about 30 seconds. Add the tomatoes with their juices and the olives and simmer, using a wooden spoon to scrape up any browned bits in the pan and blend them into the sauce. Cook for about 5 minutes to blend the flavors.

Reduce the heat to medium low and stir in the chicken and any juices. Season with salt and pepper to taste. Stir in the basil and serve immediately, topped with the freshly grated cheese.