Prepare the chicken by seasoning with salt and pepper.
In a large pot, heat some oil over medium heat and sauté the onions and garlic until translucent.
Add the carrots and celery; cook for another 5 minutes until softened.
Pour in the chicken broth and add the diced tomatoes, thyme, and prepared chicken.
Bring to a boil, then reduce heat and simmer for about 20 minutes.
Remove the chicken, shred it into bite-sized pieces, and return it to the pot.
Stir in the heavy cream and adjust seasoning if necessary.
Garnish with fresh parsley before serving.