Cut chicken into 1 1/2" cubes and sprinkle with a pinch of salt and pepper.
Heat olive oil plus a tablespoon of the lemon juice in a 12" skillet over medium-high heat. Add chicken to the skillet in a single layer.
Brown chicken on all sides (about 1 minute per side). Chicken does not need to be cooked through.
Stir in cream, chicken broth, water, lemon juice, lemon zest, pasta and garlic. Bring to a boil and reduce heat to medium. Continue to boil, stirring often, until pasta is tender; about 11-13 minutes (depending on the type of pasta this time could vary - a good rule of thumb is to follow the time on the box and add a minute or two). *If the water seems to evaporate too quickly, add another 1/2 cup of warm water to the pasta. You can always drain it if necessary.
When the pasta is tender, remove the skillet from the heat and stir in the cream cheese and Parmesan cheese until combined and smooth. Stir in capers.
Divide into bowls and serve hot. Garnish with fresh chopped flat leaf parsley, if desired.