Turn the Instant Pot® on. Choose the Sauté program and the More setting.
While the Instant Pot® is heating, coat the chicken with the flour, black pepper, salt and Italian seasoning.
When the Instant Pot® is hot, add 1 teaspoon of the olive oil. Heat for 20 seconds, then add the chicken breast. Cook for about 3 minutes on either side or until it begins to brown. Remove the chicken.
Add the remaining olive oil, carrot, and celery and cook for 2 minutes. Add the garlic and cook for an additional 30 seconds. Add the vinegar and stir well, incorporating any food that has stuck to the bottom of the pot.
Turn the Sauté program off. Return the chicken to the pot and pour in the tomatoes and water. Add the olives.
Close the lid and the vent. Select the meat and Stew program and cook for 10 minutes.
Serve in a bowl along with bread for dipping into the sauce.