Prepare the meatballs: Combine all ingredients in a large bowl. Use a 1 tsp. measure to scoop out the mixture. Using clean hands, roll the chicken mixture into a ball. Wet hands frequently, as necessary. You should finish with about 80 meatballs.Set meatballs aside on a large baking sheet or piece of parchment paper or aluminum foil.
Heat oil over medium heat in a large Dutch oven or large pot.
Cook the celery, carrots, onions, salt and pepper in the oil until they are softened, about 7-10 minutes.
Add the chicken breasts and chicken stock. Bring to a boil over medium-high heat, then reduce heat and simmer 10 minutes.
Remove the chicken from the pot and place it onto a work surface.
Drop meatballs into the simmering broth. Simmer until meatballs rise to the top, about 20-25 minutes.
While the meatballs are cooking, shred the chicken breasts into pieces with forks.
When the meatballs are cooked, add the chicken back into the pot. Add the pastina. Simmer 15 more minutes.