Soak wood chips in water for 30 minutes.

Preheat a smoker to 250°F (120°C) according to manufacturer's directions.

Place chicken, unstacked, onto wire racks. Place racks into the smoker. Transfer soaked wood chips to an aluminum pan, cover with foil, and poke holes for smoke to escape. Add pan to smoker according to instructions.

Smoke chicken until no longer pink and internal temperature reaches 165°F (74°C), about 30 to 60 minutes. Transfer to plate to cool.

Cook bacon in a skillet over medium-high heat until evenly browned, approximately 10 minutes. Dice and set aside.

Dice cooled chicken.

Cook fettuccine in salted boiling water until al dente, about 8 minutes. Drain and set aside.

Melt 1 tablespoon butter in skillet. Add garlic and cook for 30 seconds, then add mushrooms and sauté until soft (5–7 minutes).

Transfer mushrooms to a plate. Add wine to skillet, bring to a boil, and scrape up browned bits. Add ½ cup butter until melted, then stir in cream. Pour sauce into emptied pasta pot.

Slowly melt in Parmesan and mozzarella cheeses until combined. Heat sauce over medium-low heat until thickened (5–7 minutes). Season with salt and pepper.