In a large Dutch oven or heavy bottomed pot, add olive oil and cook over medium heat. Add the onions, carrots, celery, salt and pepper. Cook, stirring occasionally, until the vegetables become slightly tender, about 5-7 minutes. Add the garlic and cook until fragrant, 1 more minute.

Move the vegetables to the sides for the pot, add the chicken breasts in the middle and season with salt, pepper and thyme. Cook undisturbed for 5 minutes, then flip the chicken to the other side and add the water. Bring the mixture to a boil, then reduce the heat to medium-low and simmer, covered, until the chicken is cooked through, about 25 minutes.

Remove the chicken to a cutting board and cut into small cubes. Return the chicken back to the soup along with the rice, tomatoes and zucchini. Continue to cook the soup uncovered over medium-low heat until the rice is tender and the broth is reduced, about 30 minutes. Remove from the heat and stir in the dill and lemon juice.