Sprinkle chicken with salt and pepper. In a large skillet, brown chicken on both sides in butter. Remove from the skillet and keep warm.
Add broth and sherry (or more broth) to the skillet, stirring to loosen browned bits from the pan. Stir in the preserves, garlic and tarragon. Bring to a boil. Reduce heat; simmer occasionally. Stir in vinegar.
Return chicken to the skillet; cover and cook over medium heat for 8-10 minutes or until a meat thermometer reads 170 degrees.