Pat the chicken thighs dry with paper towels and season generously with salt, pepper, and half of the tarragon.
Heat a tablespoon of olive oil in a skillet over medium-high heat until shimmering and just starting to smoke.
Place the chicken thighs skin-side down into the hot skillet, carefully laying them away from you to avoid splatters.
Sear the chicken without moving for about 6-8 minutes until the skin is golden brown and crispy, then flip and cook for another 6-8 minutes until cooked through.
Transfer the chicken to a plate and set aside; leave the rendered fat and oil in the pan.
Trim and roughly chop the asparagus, then add it to the skillet with the remaining tarragon, stirring to coat in the flavorful fat and oil.
Sauté the asparagus for 3-4 minutes, until bright green and slightly tender, making sure to scrape up any browned bits from the pan.
Nestle the chicken thighs back into the skillet among the asparagus, skin-side up, and cook for an additional 2-3 minutes to reheat and meld the flavors.
Check that the chicken is cooked through—juices should run clear—or use a meat thermometer. Sprinkle with a little extra tarragon if desired.
Remove from heat and let rest for a couple of minutes before serving; the chicken skin will stay crispy, and the asparagus will be tender but still vibrant.
Serve the skillet directly at the table, spooning the fragrant, herby juices over the chicken and vegetables for a comforting, flavorful meal.
