Preheat an outdoor grill for medium heat and lightly oil the grate. Season both sides of the chicken breasts with salt and pepper.
Cook on the preheated grill until no longer pink in the centers and the juices run clear, about 8 minutes on each side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let rest for 5 minutes before slicing into strips.
Heat olive oil in a large pan over medium-high heat. Add onion and cook, stirring frequently, until soft and translucent, about 5 minutes. Add diced tomatoes, chicken broth, balsamic vinegar, and basil. Bring to a boil; reduce heat to a simmer and cook for 5 minutes. Season with salt and pepper.
Mix water and cornstarch together in a small bowl and slowly add to the balsamic sauce. Stir until thickened. Toss chicken strips in balsamic sauce and serve.