In a 12-inch nonstick skillet heat the 2 tablespoons oil over medium-high heat Evenly layer potatoes and carrots in skillet. Cook, uncovered, 5 minutes, until potatoes are golden, turning once. Add mushrooms and onion. Cook 5 to 6 minutes, until vegetables are crisp-tender, stirring often. Add garlic and asparagus; cook 3 minutes. Transfer vegetables to bowl; set aside.
In same skillet, heat the remaining 1 tablespoon oil. Sprinkle chicken with half the salt and pepper. Cook chicken in hot oil about 3 minutes, until lightly browned, stirring occasionally. Add broth; bring to boiling. Reduce heat. Simmer, covered, about 3 minute or until no pink remains. Increase heat to medium-high. Stir in cooked vegetables; heat through. Stir in tarragon and remaining salt and pepper. Makes 4 servings.