Season the chicken with salt and pepper.
Heat the olive oil in a pot over medium-high heat. Working in batches, add the chicken to the pot and cook until browned (2 to 3 minutes per side). Remove the chicken to a plate.
Add the celery, carrots, garlic, onion to the pot and cook, stirring for 1 minute. Add the broth, rice and stir. Add the chicken and any juices from the plate.
Add the rosemary and thyme; cover with a lid and simmer for 25 minutes.
Remove the chicken from the pot and shred with two forks pulling in opposite directions.
Meanwhile, in a small bowl, mix together the melted butter and flour with a fork to make a paste.
Return the chicken to the pot. Add the butter/flour mixture, stirring to thicken. Add the cream and bring to a simmer for 5 minutes. Just before serving, stir in the lemon juice. Taste and adjust the seasoning with salt and pepper.
Ladle into bowls with the proper ratio of broth to the rest of the ingredients. Serve with bread.