Sprinkle chicken evenly with pepper and 3/4 teaspoon of the salt. Heat oil in a large skillet over medium-high. Add chicken. Cook until well browned, about 6 minutes per side. Transfer to a plate; set aside.

Melt butter in pan over medium-high. Add mushrooms. Cook, undisturbed, 3 minutes. Stir in garlic. Cook, stirring occasionally, 3 minutes. Sprinkle with remaining 1/2 teaspoon salt. Stir in wine and stock.

Return chicken to pan, and sprinkle with thyme. Cook, undisturbed, until a thermometer inserted in thickest portion registers 165°F, about 3 minutes. Sprinkle with parsley. Serve with rice and lemon wedges.