Coat the bottom of a large pot with olive oil and place it over medium heat.
Give the oil a minute to heat up, and then add the onion, carrot, and celery. Sweat the veggies for about 10 minutes, until they begin to soften up.
Add the garlic and cook for about 1 minute more, until very fragrant.
Stir in the broth, tomatoes, chickpeas, and rosemary.
Bring the liquid to a boil, reduce the heat, and allow it to simmer for about 10 minutes.
Stir in the pasta and bring the liquid back up to a boil.
Allow the pasta to cook in the soup at a low boil until al dente — this may take a minute or two longer than the time indicated on the pasta's package directions. Stir the pot occasionally while it simmers.
Remove the pot from the heat and season with salt and pepper to taste.
Ladle into bowls and serve.