Preheat oven to 375°F. Toss carrots, almonds, honey, and 2 tablespoons oil on a large rimmed baking sheet; season with salt and pepper. Roast, tossing occasionally, until carrots are tender, 15-20 minutes.
Meanwhile, heat remaining 2 tablespoons oil in a large skillet over medium-high heat. Season chicken with salt and pepper. Cook chicken, skin side down, until golden brown, 5-8 minutes. Turn chicken over, transfer skillet to oven, and roast until cooked through, 10-15 minutes longer.
While chicken and carrots are roasting, mix yogurt and lemon juice in a small bowl. Season with salt and pepper.
Remove chicken and carrots from oven; transfer chicken to a large plate. Add carrots, shallot, and tarragon to skillet and toss to coat in pan drippings. Serve with lemon yogurt.