Heat oil in a large pot over medium high heat.  Add in celery, carrots, and onion and saute until softened, about 5 minutes.  Add in garlic and cook an additional 30 seconds.  

Season chicken breasts with salt and pepper.  Add to pot along with chicken broth.  Bring to a boil, then simmer for 20 minutes, until chicken is no longer pink in the middle.  Pull chicken out, shred with a fork, then return to the pot. 

In a medium bowl, combine flour, baking powder, and salt.  In another bowl, combine milk and butter.  Add milk/butter mixture to flour mixture and mix just until combined.  

Drop dough by the teaspoon into the soup, then cover and let simmer an extra 20 minutes.