Heat 1 tablespoon olive oil in a large stockpot over medium heat. Season chicken with salt and pepper, to taste. Add chicken to the stockpot and cook until golden, about 2-3 minutes; set aside.
Add remaining 1 tablespoon oil to the stockpot. Add garlic, onion, carrots and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Stir in thyme and rosemary until fragrant, about 1 minute.
Pour in chicken stock, bay leaf and 2 cups water; bring to a boil. Stir in zucchini “noodles”; reduce heat and simmer until zucchini is tender, about 3-5 minutes. Season with salt and pepper, to taste.
Dice chicken and return to the pot and stir until combined and warmed through.