1) Drizzle chicken with olive oil, salt and pepper. Grill chicken until cooked through on medium-high heat. It should take about 18 minutes, but could vary based on the size of your chicken breasts. Be sure to turn the breasts once halfway through cooking.
2) Cook pasta according to package. Reserve a cup of cooking water.
3) For sauce, grate Parm in a large bowl. Melt butter in medium sauce pan over medium heat.
4) Once butter is melted, stir in cream and continue to stir until sauce starts to thicken, about 4-5 minutes.
5) The sauce is done when you can leave a streak in it with a spatula.
6) Pour sauce over grated cheese and let sit for 2 minutes. Season with salt and pepper.
7) Add drained pasta to bowl and toss well to combine.
8) Serve immediately with sliced chicken.