Cook pasta in salted boiling water, according to package instructions, until al dente. Drain, but reserve pasta water.
Cook Chicken: Season chicken with salt and pepper. Heat a skillet over medium heat. Once hot, add olive oil. Once olive oil is hot, add chicken and cook until browned, turning once, until cooked through (165 degrees). Remove to a plate to rest for a few minutes, before chopping into pieces.
Sauce: Add butter to pan and fry shallots for 1 to 2 minutes, stirring constantly. Reduce heat to low. Add 1 cup reserved pasta water to the pan and scrape up any browned bits. Whisk in Boursin cheese until melted and smooth.
Serve: Add cooked pasta and chicken to the pan and toss to evenly coat in sauce. Add a splash of pasta water, if needed, to thin the sauce. Season with salt and pepper, if needed. Garnish with fresh parmesan and parsley.