How to Make It
Heat the oven to 375 F degrees. Pierce each fig three or four times with a paring knife. In a small stainless-steel saucepan, combine the figs, water, the 2/3 cup port, and the lemon zest. Bring to a boil and simmer, covered, until tender, about 30 minutes. Discard the zest and reserve the poaching liquid. Cut the figs in half.
Meanwhile, coat the chicken with the oil and arrange the pieces, skin-side up, in a large roasting pan. Sprinkle the chicken with the remaining 1 tablespoon port and season with 1/4 teaspoon salt and 1/8 teaspoon pepper. Top each piece of chicken with a piece of the butter. Cook until the breasts are just done, about 30 minutes. Remove the breasts and continue to cook the legs until done, about 5 minutes longer. Remove the roasting pan from the oven; return the breasts to the pan.
Heat the broiler. Broil the chicken until the skin is golden brown, about 2 minutes. Transfer the chicken to a plate.
Pour off the fat from the roasting pan. Set the pan over moderate heat and add the fig-poaching liquid. Bring to a boil, scraping the bottom of the pan to dislodge any brown bits. Boil until reduced to approximately 1/4 cup, about 4 minutes. Add the figs, any accumulated juices from the chicken, and a pinch each of salt and pepper. Spoon the sauce over the chicken.