In a large pot, bring salted water to a boil, and cook the spaghetti noodles.
In a large not non-stick skillet, melt the butter and thyme over medium heat. Add the sliced mushrooms to the skillet, and stir to coat in butter. Leave them to cook for a few minutes until a nice crust forms and turn golden brown.
Remove the mushrooms alone from the pan and add oil to the butter and thyme mixture in the pan.
Salt and pepper both sides of the chicken breasts.
Turn the heat up to medium-high, and sear the chicken breasts on both sides in the same pan that the mushrooms were in. Cook until so that a good crust forms. Remove the chicken from the pan, and cover to keep warm.
Turn the heat down to low and add all of the wine. Allow the wine to cook just a bit and make sure you scrape any food stuck to the pan.
Dice the cream cheese and place in a large bowl. Discard the thyme sprigs from the pan, and then pour the hot wine over the cream cheese and stir until it melts.
When the pasta is done, drain it, and immediately pour it over the wine-cream cheese mixture. Toss the noodles to melt and evenly distribute the cream cheese sauce.Stir the mushrooms into the pasta bowl.
Slice the chicken and garnish on top. Serve warm.
