Pat the chicken breast fillets dry with paper towels, cut into bite-sized pieces, and season with salt and pepper on all sides. Coat lightly with flour and shake off excess.
Heat 6 tablespoons of olive oil in a large pan over medium-high heat for 2 minutes until shimmering.
Working in batches to avoid crowding, fry the chicken pieces for 4-5 minutes per batch over medium-high heat until golden brown on all sides. Transfer each batch to a plate.
Pour out most of the oil from the pan, leaving about 1 tablespoon. Add 125 ml sherry and 200 ml chicken broth, scraping up any browned bits from the bottom with a wooden spoon.
Stir in 2 crushed garlic cloves and three-quarters of the chopped thyme. Reserve the remaining thyme for garnish.
Return the chicken pieces to the pan. Simmer over low heat for 10 minutes until the chicken reaches 74 °C (165 °F) at the thickest part.
While the chicken simmers, slice the pepper-filled olives. During the last 2 minutes of cooking, add the sliced pepper-filled olives and black olives to the pan and stir gently.
Serve the chicken with sauce in bowls, garnished with the reserved thyme.