1/2 lb fatty salt pork, salt rinsed off (if necessary) and cut into 1/2-inch cubes
1 (3 1/2- to 4-lb) chicken, cut into 8 serving pieces
2 tsp Kosher Salt
1 tsp Black Pepper
1 Tbsp unsalted butter
1 lb onions, cut into 1/2-inch pieces
2 medium carrots (1/2 lb), cut into 1/2-inch cubes
1/2 tsp Dried Savory, Whole Leaf, crumbled
1 Tbsp all-purpose flour
6 Cups water
2 lb boiling potatoes
Cook pork in a wide 6- to 7-quart heavy pot over moderate heat, stirring, until golden and fat is rendered, about 8 minutes. Transfer pork with a slotted spoon to paper towels and pour off all but about 2 Tbsp fat from pot.
Pat chicken dry and sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper. Brown chicken in pork fat in heavy pot, over moderately high heat. Do the chicken in 2 batches, skin sides down first and turning over once, about 6 minutes per batch. Transfer chicken to 2 plates, breast pieces on one platter and the remainder on the other.
Add butter to fat in heavy pot, then cook onions, carrots, and savory over moderately low heat, stirring, until vegetables are softened, about 10 minutes. Add flour to mixture and cook, stirring, 1 minute. Add water in a stream, whisking, then add remaining teaspoon salt and 1/2 teaspoon pepper. Bring entire mixture to a boil over high heat.
Return chicken, except breast pieces, and salt pork to pot. Reduce heat to a simmer, and cook, partially covered, about 20 minutes. Be sure to stir stew occasionally during this time.
Peel potatoes and cut into 3/4-inch cubes. Add potatoes and chicken breast pieces to stew pot, then simmer, partially covered, until chicken is cooked through and potatoes are tender, about 15 minutes.