Heat oil in a large soup pot over medium high heat.
Add carrots, celery and onion and cook until softened, about 4-5 minutes, stirring often.
Add garlic, parsley, salt, thyme and pepper and cook 1 minute.
Add chicken broth, chicken breasts and rice. Bring to a simmer, cover and reduce heat. Cook for 30-40 minutes, until rice is tender.
Remove chicken and shred, then stir back in.
Whisk together the cream and corn starch and stir into the soup. Cook and stir until thickened.
