Bring a large pot of lightly salted water to a boil. Add pasta, and cook for 8 to 10 minutes or until al dente; drain.
Heat oil in a skillet over medium heat. Dredge chicken cubes in flour seasoned with salt and pepper, and brown in the hot oil. Once the chicken is browned on all sides, squeeze the juice from one lemon over the cubes. Stir in the capers, olives and anchovy paste, and cook for at least 5 minutes to mingle the flavors, and cook the chicken.
When chicken is no longer pink, add the diced tomatoes, juice from the remaining lemon, salt, and pepper. Add pasta and cheese to the pan, and cook, stirring just until heated through.
