Drizzle about half the olive oil into a small skillet over medium heat. Add the sliced tomatoes and sprinkle with salt and pepper. Stir occasionally and allow the tomatoes to soften. A little char is desirable, but watch so they don't burn.
Sprinkle the chicken with salt, pepper, and Italian seasoning. Heat a cast-iron or iron skillet over medium-high heat. Add the chicken breast and cook undisturbed on the first side. for about 5-7 minutes. Flip and allow the chicken to cook through completely. The length of time will vary based on the thickness of the meat, typically about 15 minutes.
Plate the chicken. Arrange the tomatoes over the top of each piece of chicken. Separate the burrata ball in half by tearing your hands. Sprinkle with fresh basil and serve.