Bring a large stockpot of water to boil. Add pasta and cook until al dente, about 10-12 minutes. Drain pasta, reserving 1 cup pasta water, and return pasta to pot.
While pasta is cooking, heat olive oil over medium-high heat. Add chicken breast, season with salt and pepper, and cook, 4-6 minutes per side until chicken is cooked through. Remove from pan and shred chicken with two forks.
In the same pan, add butter and mushrooms and cook, 4 minutes until mushrooms are slightly soft.
Add chicken back to pan along with heavy cream and parsley. Stir to combine, bring to boil, then reduce heat and simmer for 5 minutes.
Remove pan from heat and toss with pasta and 1 cup reserved pasta water.
Divide evenly among bowls or plates and top each with equal amount of parmesan cheese and truffle oil. Serve immediately.