Heat olive oil in a large pot over medium heat. Add the onions, celery, and carrots and cook for 3-4 minutes. Stir in the garlic and cook until fragrant.
Once it comes to a boil, cover, reduce the heat to medium, and cook for 20 minutes. Once done, remove the chicken from the pot and shred using two forks or an electric mixer.
Place the shredded chicken back into the pot along with the ditalini pasta. Cook until the pasta is al dente. Turn off the heat and season generously with salt and pepper.