Pat chicken dry with paper towels and season with salt and pepper on all sides.
Heat oil in a large Dutch oven or soup pot over medium-high heat until shimmering. Add the chicken and cook until browned on both sides, about 6 minutes per side. Remove chicken to a plate.
Leave about 1 tablespoon of fat in the pot; drain off the rest. Saute the onion, celery and carrots in the same pot over medium-high heat until softened, about 5 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds.
Add bay leaf, thyme, rosemary and chicken stock. Return chicken to the pot. Bring to a boil over high heat. Reduce heat to medium-low and simmer until chicken is tender and cooked through, about 35-40 minutes.
Remove chicken to a large bowl to cool. Keep broth warm in the pot. When the chicken is cool enough to handle, remove the meat from the bones and chop or shred into bite-sized pieces. Discard the skin and bones.
Return shredded chicken to the pot with the broth. Discard bay leaf. Taste and season the broth with salt and pepper. Stir in the cooked rice and warm over low heat, just until the chicken and rice are hot.
Remove from the heat and stir in parsley and lemon juice. Ladle into individual bowls and serve!