Add the olive oil and butter to a large pot and saute the onion and garlic over medium heat on the stove-top. Continue stirring until the onion has softened and is translucent (approximately 3 minutes).
Add the carrot and celery and cook for a further 3 minutes.
Add the parsley, thyme, bay leaf, chicken stock liquid and water, and stir.
Add the whole chicken breasts and stir, then cover with a lid and allow to cook, just simmering, for 30 minutes (stirring occasionally).
Add the rice, stir and cover again. Cook for a further 15 minutes.
Remove the chicken breasts from the soup and place onto a plate. Using two forks, shred the chicken into pieces. Return the shredded chicken meat to the soup to reheat through.
Discard the bay leaf. Season with salt and pepper and serve.