Add the olive oil to a medium pot over medium heat. When warm, add the celery, carrot, and onion. Stir to coat and cook for 2 minutes, or until just starting to soften.
Add the broth and raise the heat to high. When the broth starts to boil, turn down the heat to medium so it simmers. Simmer for 4 minutes.
Blend the broth very smooth in a blender.
Return broth to the pot over low heat.
Add the pasta. Cook for about 8 minutes, stirring occasionally.
Stir in the chicken.
Turn off heat and add optional flavor enhancers. Add more broth as desired and serve.
Notes
Store leftovers in an airtight container for up to 5 days in the fridge. Warm in a heat-safe bowl in a small pot or in the microwave, adding broth if desired.
Make this easier by starting with pre-cut mirepoix from the produce or freezer aisle of your supermarket. Or make homemade mirepoix and stash it in the freezer.
Simmer Parmesan rind in the broth for extra flavor.