Season your chicken breasts with a pinch of salt on both sides, and set aside.
In a large pot, combine olive oil and butter. Place the pot over medium heat to melt the butter and heat the oil. Once heated, add your chicken to the pot. Sear the chicken for about 3 to 5 minutes on each side, or until golden brown. The chicken doesn't need to be fully cooked at this point.
Transfer your chicken to a plate, and set aside. If needed, add another tablespoon of olive oil to your pot. Add your diced onion, along with the remaining salt. Still on medium heat, cook the onion until it turns translucent (about 2 to 3 minutes).
Add the remaining ingredients to the pot (excluding the parsley) along with the cooked chicken. Turn your heat up to high, and bring the soup up to a boil. Reduce the heat to medium-low, and simmer your soup for 20 to 25 minutes, or until the rice and chicken are fully cooked, and your carrots have softened.
Take your chicken out and shred it, discarding the bones. Return the shredded chicken to the soup, along with the parsley. Stir to combine. Taste for seasoning, and adjust if needed. Remove the cinnamon stick, and serve! *** (see notes)