In a large soup pot, heat oil briefly over medium heat. Add celery, onion, and carrots. Cook for 5 minutes, stirring occasionally to prevent browning.
Add broth, chicken, and dried parsley. Cover and bring soup to a simmer. Simmer for 5 minutes, and then increase heat to bring soup to a boil. Once boiling, add pasta and continue gently boiling (covered) until pasta is done (following time recommendation on pasta package).
Taste and season with salt, as needed, so the flavors pop. (This can vary a bit depending on your brand of chicken broth, but we find approximately 3/4 teaspoon typically works well.) Garnish with fresh parsley if desired.
Chicken: A standard grocery store rotisserie chicken should yield about 2 cups of chopped or shredded breast meat. But, there is definite variation, and if your bird is a bit on the smaller side, you may need to also include a little dark meat to yield 2 full cups.
Make-ahead and freezing tips: You can chop the vegetables and chicken earlier in the day or the day before, covering and refrigerating vegetables and chicken separately until you're ready to make this soup. In addition, this soup rewarms well later. The noodles will soften a bit more upon standing, but are still delicious. In addition, this soup also freezes well.