Preheat your oven to 400°F (200°C). Place the sheet pan in the oven while it heats so it gets hot enough for roasting.
Pat the chicken breasts dry and rub them all over with 1 tablespoon of olive oil, then season generously with salt, pepper, and chopped tarragon.
4 pieces chicken breasts
Carefully remove the hot sheet pan from the oven and arrange the chicken breasts on it. Return the pan to the oven and roast for about 10 minutes.
4 pieces chicken breasts
While the chicken begins roasting, trim the tough ends off the asparagus and toss them with the remaining 1 tablespoon of olive oil, salt, pepper, and a sprinkle of tarragon.
4 pieces chicken breasts
After the initial 10 minutes, carefully add the asparagus to the sheet pan around the chicken, spreading them so they cook evenly, then return the pan to the oven to roast for another 10 minutes.
4 pieces chicken breasts
Remove the sheet pan from the oven once the chicken is cooked through (internal temperature should reach 165°F) and the asparagus is tender and lightly browned. Let the chicken rest for a few minutes before slicing.
4 pieces chicken breasts
Slice the chicken breasts and serve alongside the roasted asparagus, garnished with extra tarragon if desired for a fragrant finish.