Preheat oven to 400 degrees. Heat olive oil in a 12-inch skillet over medium-high heat. Sprinkle chicken thighs with salt and pepper. Place thighs, skin side down, in hot oil, and cook until skin is golden brown, about 10 minutes. Flip thighs, and cook until other side is brown, about 5 minutes. Transfer chicken to a plate.
Add potatoes to skillet and toss to coat in oil. Return chicken to skillet. Place skillet in preheated oven, and roast until potatoes are almost done, 12 to 51 minutes. Add asparagus and peas to skillet, tossing to coat. Continue roasting until a thermometer inserted in thickest portion of thighs registers 165 degrees and the vegetables are tender, 3 to 4 minutes more.
Prepare the Shallot Vinaigrette: Whisk together oil, red wine vinegar, shallot, mustard, salt, and pepper in a small bowl. Drizzle vinaigrette over chicken thighs and vegetables, and sprinkle with tarragon. Serve immediately.