In a large soup pot, sauté the finely chopped celery, carrots, and onions with the butter and olive oil over medium-high heat. Cook for 5-7 minutes or until the vegetables become tender.
Stir in the minced garlic, and cook for about 30 seconds or until fragrant. Then, add the flour. Continue to cook for another minute or until the flour is lightly browned.
Pour in the chicken broth, and stir well until the flour has dissolved into the broth. Add the oregano, thyme, salt, black pepper, and bay leaves to the pot.
Place the uncooked chicken breasts and washed rice into the pot. Bring the soup to a boil, then reduce the heat to a simmer. Cover and let it simmer for 20-25 minutes, or until the chicken is fully cooked and the rice is tender.
Remove the chicken breasts from the pot and cut them into bite-sized pieces. Return the chicken pieces to the soup.
Squeeze a bit of lemon juice into the soup to brighten the flavors. Adjust the taste with salt and pepper, if needed.
Just before serving, sprinkle chopped fresh parsley over the soup for added freshness and color.
Ladle the chicken and rice soup into bowls and enjoy!
Store in an airtight container in the fridge for up to 3 days, or freeze for up to 3 months.