Place chicken in 9-inch pie plate. Brush both sides with 1 tablespoon olive oil. Remove stems from basil, oregano and rosemary. Place herb leaves on plate; cover with damp paper toweling; refrigerate until ready to use. Scatter herb stems and 2 teaspoons garlic over chicken. Cover; refrigerate 1 hour.
Cut each mushroom in half or quarters if very large. Place in medium-size bowl. Stir in 2 teaspoons oil, the vinegar, remaining 1 teaspoon garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper. Cover; refrigerate 1 hour.
Remove chicken from pie plate; discard stems. Chop reserved herb leaves; place on waxed paper. Sprinkle chicken with remaining salt and pepper. Dip chicken into herbs, coating both sides evenly.
Heat 1 tablespoon oil in large nonstick skillet over medium-high heat. Add chicken; cook until browned on both sides and no longer pink in center, about 3 minutes per side. Transfer chicken to serving platter; keep warm.
Heat remaining 1 teaspoon oil in nonstick medium-size skillet over medium heat. Add mushrooms and any remaining liquid; cook until tender, 3 to 4 minutes.
Arrange mushrooms around chicken. Garnish with basil.