Preheat your oven to 400°F (200°C). Line a sheet pan with parchment paper for easy cleanup.
Pat the chicken breasts dry with paper towels and place them on the prepared sheet pan. Drizzle with a tablespoon of olive oil and rub to coat evenly, then season with salt, pepper, and half of the tarragon.
Trim the woody ends off the asparagus and scatter the spears around the chicken on the pan. Drizzle the remaining olive oil over the asparagus and sprinkle with the rest of the tarragon, a pinch of salt, and pepper.
Place the sheet pan in the oven and roast for about 20 minutes, or until the chicken is cooked through and juices run clear, and the asparagus is tender with lightly browned tips.
Remove the sheet pan from the oven and let the chicken rest for a few minutes. The vegetables will have absorbed the flavors and developed a nice roasted aroma.
Slice the chicken breasts if desired and serve alongside the roasted asparagus, garnished with a few extra tarragon leaves if you like. Enjoy the simple, fragrant flavors of this wholesome dish.