"I prepare this dish inside on my stovetop gas grill in winter and outdoors on my gas or
charcoal grill in summer. Make sure your grill is very clean, or the chicken will stick. The
bird is grilled long enough so that most of the fat in the skin drains away, and it is then
transferred to a warm oven to finish cooking in its own juices. A delicious tarragon butter,
dotted on the chicken at serving time, replicates the flavor of a bearnaise sauce."
Preheat an outdoor grill for medium-high heat. Preheat oven to 160 degrees F (71 degrees C).
Spread 1 tablespoon olive oil and 1/2 teaspoon salt over the chicken pieces.
Place chicken pieces skin-side down on the hot grill; cook until browned, turning occasionally, about 20 minutes for the breasts and 30 minutes for the leg pieces. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Transfer to a baking sheet and keep warm in the preheated oven.
Combine remaining 1 1/2 tablespoon olive oil, remaining 1/4 teaspoon salt, butter, tarragon, and lemon juice in a food processor; blend until smooth.
Divide grilled chicken pieces among 4 serving plates. Dot each serving with about 1 tablespoon of the tarragon butter.