Season the chicken on both sides with about 1 tsp. salt and 1/2 tsp. pepper. Heat 2 tsp. of the oil in a 12-inch skillet over medium-high heat until hot. Working in two or three batches to avoid crowding, cook the chicken until lightly browned on both sides and just cooked through, 1 to 3 minutes per side. Transfer each batch of chicken to a platter, cover loosely with foil, and keep warm. If the pan seems dry at any point, add 2 more tsp. of oil.
Reduce the heat to medium, add 2 tsp. oil, and then the onion. Cook, stirring occasionally, until the onion softens, about 3 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Add the sherry and chicken broth, increase the heat to medium high, and cook until the sauce thickens slightly, about 3 minutes. Stir in the olives and cook until heated through, about 1 minute. Stir in the parsley, season to taste with salt and pepper, and spoon the mixture over the chicken. Sprinkle with the almonds and serve.
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