Clean, stem, and slice mushrooms; set aside.
In a large, heavy-bottomed skillet, heat butter and oil on medium-high setting.
Sprinkle salt and pepper over chicken breasts. In a shallow bowl, dredge breasts in flour. Shake off excess; then place chicken in hot skillet. Cook without moving until browned on one side (about 3 minutes); then flip and brown other side. Reduce heat to medium.
Add garlic and mushrooms. Cook, stirring occasionally, until mushrooms are golden and fragrant, about 3 minutes. Add wine and increase heat to high. Cook until wine has reduced by half, about 5 minutes.
Lower heat to medium and slowly stir in cream and all but a generous pinch of thyme. When chicken is cooked through (cut to test), remove from heat. Just before serving, squeeze lemon juice over chicken, check seasonings, and garnish with reserved thyme.