Heat the oil in a large skillet over medium heat. Sprinkle the chicken with ⅛ teaspoon salt and ¼ teaspoon pepper.
Sauté the chicken until cooked through, 8 to 10 minutes per side. Remove from skillet, cover, and set aside.
Add the sweet potato and ½ cup water to the skillet and cook over medium heat, stirring, about 5 minutes.
Add the pear and cook for 5 more minutes or until the potato is tender.
Transfer to a bowl. Toss with the vinegar, mustard, tarragon, ⅛ teaspoon each salt and pepper, and 3 tablespoons of water.
Divide the chicken among 4 plates. Spoon the vegetables over each entrée.