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.
Traditional stovetop braises rely on long simmer times to develop depth, whereas pressure cooking accelerates tomato breakdown by using sealed steam. Developing deep flavors in a shorter window requires precise control over the initial searing phase. Dredging the chicken breast in two teaspoons of flour and seasoning before heating creates the necessary starch coating for thickening the sauce later. Sear the meat for three minutes per side on the high sauté setting until the surface turns golden brown. Fond forms on the bottom of the cooker during this step. Deglazing the pot with one teaspoon of balsamic vinegar releases those browned proteins into the liquid, which prevents the unit from triggering a burn warning. Carrots and celery require exactly two minutes of sautéing to soften slightly before the liquids are added. Minced garlic burns easily, so incorporate it during the final thirty seconds of the vegetable sautéing phase and stir constantly. Lock the lid securely and select the meat and stew program for a ten-minute pressure cycle. Electric multi-cookers substitute efficiently for traditional heavy-bottomed Dutch ovens by maintaining consistent pressure and temperature without requiring constant manual adjustment. Natural pressure release is not utilized here; instead, manual venting finishes the cycle quickly. Serve the finished stew immediately with a slice of sprouted whole-grain bread positioned to absorb the acidic tomato broth.