Bring a large pot of salted water to a boil. Add the potato gnocchi and cook according to package instructions until they float to the surface, about 2-3 minutes. Drain and set aside.
Heat olive oil in a large non-stick skillet over medium heat. Add the chopped onion, carrot, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the minced garlic, dried thyme, and dried oregano to the skillet. Cook for 1 minute until fragrant.
Add the chicken pieces to the skillet. Season with salt and black pepper. Cook, stirring occasionally, until the chicken is cooked through and no longer pink in the center, about 6-8 minutes.
Pour in the low sodium chicken broth and bring to a simmer. Add the sliced mushrooms and cook for 4-5 minutes until mushrooms are tender.
Stir in the chopped fresh spinach and cooked gnocchi. Cook for an additional 2 minutes until the spinach wilts and everything is heated through.
Taste and adjust seasoning with additional salt and pepper if needed.
Remove from heat and sprinkle with chopped fresh parsley before serving.