Place the chicken in a pot of boiling water or broth and cook until tender, about 15 minutes. Remove, shred the chicken with two forks, and set aside.
Heat olive oil in a large heavy-bottomed pot over medium heat. Add diced onions and minced garlic, sauté until fragrant and translucent, about 5 minutes. The onions should become soft and slightly golden.
Add chopped carrots and celery to the pot. Cook, stirring occasionally, until the vegetables start to soften, about 7 minutes. The vegetables should develop a slight sheen and become tender but still retain some crunch.
Pour in the chicken broth and bring the mixture to a gentle simmer. Once simmering, add the shredded chicken and dried thyme. Let the soup simmer gently for about 10 minutes to meld the flavors.
Taste the broth and season with salt and pepper as needed. Squeeze in fresh lemon juice to brighten the flavor. Continue to simmer for another 2-3 minutes to let the flavors combine.
Serve the hot soup in bowls, garnished with freshly chopped parsley for a burst of freshness and aroma. Enjoy the comforting, vibrant flavors of this bright chicken vegetable soup.