In a large saute pan, heat 2 teaspoons olive oil over medium-high heat. Add garlic and chicken to pan, sprinkle with salt and pepper, and saute 3-4 minutes, until lightly browned. Transfer to a bowl. (Make sure to get all the garlic out, or it will burn in the next stage.)
Return pan to heat, and warm the rest of the olive oil (4 teaspoons). Add shallots, mushrooms, thyme sprigs and another sprinkle of salt and pepper, and toss to coat with oil. Cook for 10-12 minutes, turning often, until mushrooms are soft and slightly gilded.
Pour wine into pan, and scrape up any bits stuck to the bottom. Let cook for 2 minutes or so, until all the liquid has burned off. Add chicken and garlic back to the pan. Pour in chicken stock, and bring to a boil for 3 minutes to thicken a bit. Pour in cream, and give everything a stir. Bring to a gentle boil for 3-4 minutes, until the sauce has thickened enough to lightly coat the back of a spoon.
Remove thyme sprigs, and serve.