Step 1

Heat the oven to 425°F with a rack in the middle position. Set a wire rack in a rimmed baking sheet. Set the chicken breast side up on the rack. Place the tarragon and lemon halves in the cavity of the chicken. Tie the legs together with kitchen twine and tuck the wing tips back. Brush the bird all over with the oil and season with salt and pepper. Roast until the thighs reach 175°F, about 1¼ hours.

Step 2

Using tongs, tilt the chicken so the juices run out of the cavity, then transfer the chicken to a cutting board; let rest for about 15 minutes. Meanwhile, remove the rack from the baking sheet; pour about half the wine onto the baking sheet or broiler pan. Scrape up any browned bits, then carefully pour the mixture into a medium saucepan; add the remaining wine. Bring to a simmer over medium and cook until reduced by about half, 8 to 10 minutes. Remove from the heat.

Step 3

Untie the chicken, then remove and reserve the lemon halves from the cavity. Carve the chicken and transfer to a platter. Return the sauce mixture to a simmer over medium, then remove from the heat and whisk in the butter until melted. Add the chopped tarragon to the sauce, then squeeze in 2 tablespoons juice from the lemon halves. Taste the sauce and season with salt and pepper. Pour any accumulated juices on the cutting board onto the chicken. Serve with the sauce.