Heat 1 tablespoon olive oil in a large stockpot or Dutch oven over medium heat. Season chicken pieces with salt and pepper, to taste. Add chicken to the stockpot and cook until golden, about 3-4 minutes; remove chicken to a bowl, cover loosely with foil and 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 until fragrant, about 1 minute.
Pour in chicken stock, water and bay leaves; bring to a boil. Stir in orzo, rosemary and chicken; reduce heat and simmer until orzo is tender, about 10-12 minutes. Remove bay leaves and rosemary sprig. Stir in lemon juice and parsley; season with salt and pepper, to taste. Serve immediately.