2 Tbsp. unsalted butter, divided in half
1/4 cup whole almonds with skins
4 boneless chicken breast halves with skin (2 1/4 pounds total)
1 cup brine-cured green olives, such as picholine, pitted and chopped
3 Tbsp. water
2 Tbsp. chopped fresh flat-leaf parsley
Salt and freshly ground black pepper
1. Heat 1 Tbsp. butter in a 12-inch nonstick skillet over moderate heat until foam subsides, then toast almonds, stirring often, until a few shades darker, 5 to 8 minutes. Transfer with a slotted spoon to a cutting board to cool (do not clean skillet).
2. While almonds are cooking, pat chicken breasts dry, then cut a 2-inch-long horizontal slit in thickest part of each. Stuff each chicken breast with 1 1/2 teaspoons olives, then season with salt and pepper.
3. Increase heat to moderately high, then add chicken breasts, skin sides down, to butter remaining in skillet and sprinkle with remaining olives. Saute chicken breasts until skins are golden brown, 8 to 10 minutes. Turn chicken breasts over and cook, covered, over moderate heat until just cooked through, 5 to 7 minutes more, then transfer with tongs to plates.
4. While chicken is cooking, chop almonds.
5. Add remaining tablespoon butter and 3 Tbsp. water to skillet and heat, stirring, until butter is melted. Stir in almonds, parsley, and pepper, to taste. Spoon sauce over chicken.