1. Place each chicken breast half between 2 sheets of heavy-duty plastic wrap, and pound to 1/2-inch thickness using a meat mallet or small heavy skillet.
2. Heat a large nonstick skillet over medium-high heat. Add canola oil to pan; swirl to coat. Sprinkle chicken with 1/4 teaspoon salt and pepper. Add chicken to pan; cook 3 minutes on each side or until done. Transfer chicken to a serving platter; keep warm.
3. Add shallots and mushrooms to pan; sauté for 4 minutes or until browned, stirring occasionally. Add garlic; sauté for 1 minute, stirring constantly. Stir in wine, scraping pan to loosen browned bits; bring to a boil. Cook until liquid almost evaporates. Sprinkle mushroom mixture with remaining 1/4 teaspoon salt and flour; cook 30 seconds, stirring frequently. Add broth to pan; bring to a boil. Cook 2 minutes or until slightly thick. Remove pan from heat; add butter and thyme, stirring until butter melts. Serve with chicken.