In a large skillet over medium heat, heat 1 tablespoon of the olive oil. Add the chicken and season generously with salt and pepper. Cook until an internal temperature of 165°F is reached, about 5 minutes per side.
Meanwhile, cook the pasta according to package directions until al dente. Drain, reserving 1 cup pasta water, and set aside.
Transfer the chicken to a plate and add the remaining ¼ cup of oil to the skillet. Add the garlic and cook 1 minute.
Add the lemon juice, zest, and red pepper flakes, as well as 1/4 cup of the reserved water – scraping all the bits on the bottom of the pan.
Add the rotini and heavy cream and toss to combine.
Serve the chicken on top of a bed of pasta, topped with parmesan cheese, a sprinkle of parsley, and a lemon wedge.