Meanwhile, heat olive oil in large deep skillet on medium-high. Season chicken with kosher salt and pepper and cook until golden brown on all sides, 4 to 5 minutes.
Add lemon juice to skillet and cook, scraping up any browned bits. Add cream cheese and stir until melted; remove from heat.
Fold in lemon zest and Parmesan, then parsley. Toss with pasta (adding reserved cooking liquid, 1 tablespoon at a time as necessary). Serve immediately.
