Heat olive oil in a large Dutch oven over medium heat. Brown the chicken thighs on both sides, then remove and set aside.
In the same pot, saute the diced onion and garlic until fragrant and translucent.
Add the butternut squash, baby potatoes, carrots, crushed tomatoes, and chicken broth. Bring to a gentle boil.
Return the browned poultry to the pot. Reduce heat, cover, and simmer for 40 minutes until the meat is tender and falls apart easily.
Shred the meat slightly with two forks right in the pot. Stir in fresh parsley, season to taste, and serve warm.