Heat olive oil in a large pot over medium heat. Cook and stir onion and garlic in hot oil until onion is soft, about 5 minutes. Sprinkle flour evenly over the onion mixture; add tomatoes, chicken broth, oregano, basil, and parsley.

Bring the liquid to a boil and cook until the tomatoes are softened, 8 to 10 minutes.

Pour soup into a blender no more than half full. Cover and hold lid in place. Pulse blender a few times before leaving on to blend. Puree soup in batches until smooth and return to the pot.

Stir chicken, heavy cream, sea salt, and pepper into the soup; simmer until the chicken is hot, about 5 minutes.