Cut each chicken breast half in half horizontally to form 8 cutlets. Heat a large skillet over medium-high heat. Sprinkle chicken evenly with 1/4 teaspoon salt and pepper. Place flour in a shallow dish; dredge chicken in flour, shaking off excess.
Add 1 tablespoon olive oil to pan; swirl to coat. Add 4 cutlets to pan; cook 2 minutes on each side or until done. Remove chicken from pan, and keep warm. Repeat procedure with 1 tablespoon olive oil and remaining 4 cutlets.
Add remaining 1 tablespoon oil to pan; swirl to coat. Add pearl onions and mushrooms; sauté 6 minutes or until browned. Remove pan from heat. Carefully add brandy to pan; return pan to medium-high heat, and bring mixture to a boil. Cook until liquid almost evaporates (about 2 minutes). Combine stock and cornstarch, stirring with a whisk until smooth. Add stock mixture to pan, stirring with a whisk; cook 2 minutes, stirring occasionally. Return chicken to pan; cook 1 minute. Remove from heat; stir in remaining 1/4 teaspoon salt, butter, and thyme.