Place the chicken breasts in the bottom of the slow cooker.
Add the diced onion, sliced zucchini, and minced garlic over the chicken.
Pour the chicken broth, olive oil, lemon juice, and lemon zest into the pot.
Sprinkle the oregano, thyme, salt, and black pepper over everything.
Cover and cook on low for 6 hours until the chicken is tender and easily shredded.
Shred the chicken with two forks directly in the pot and stir to combine with the vegetables and broth.
Ladle into bowls and top with the chopped fresh parsley before serving.