Heat olive oil in a stockpot over medium heat. Cook and stir celery, chopped onion, and bell pepper in hot oil until softened, about 5 minutes. Stir garlic into the celery mixture; cook and stir until fragrant, about 1 minute more.
Pour vegetable broth into the pot; add tomatoes, carrots, potatoes, pearl onions, thyme, salt, and pepper. Bring the broth to a boil, reduce heat to medium-low, and simmer until the vegetables are tender, about 20 minutes.
Stir chicken and red pepper flakes to the pot; cook until the chicken is hot, 5 to 10 minutes. Stir vinegar into the soup just before serving.