Steam the butternut squash until barely tender, about 10 minutes. Remove half of the squash pieces and set aside. Steam the remaining squash until very tender, an additional 4 to 6 minutes. Mash this squash coarsely with the back of a fork. Set aside.
In a large saucepan set over medium heat, add the olive oil. Add the onion and cook, stirring occasionally, until onion is starting to turn golden, 8 to 10 minutes. Add the minced garlic and oregano – cook, stirring, for 1 additional minute.
Add the diced tomatoes, butternut squash pieces, mashed butternut squash, chicken broth, and quinoa. Stir to combine. Bring to a simmer, cover and cook until the quinoa turns translucent, about 15 minutes.
Add the shredded chicken, kalamata olives, and salt and pepper to taste. Simmer, uncovered, until chicken is heated through and sauce has thickened to your liking, about 10-15 more minutes. Add more salt/pepper if needed, to taste.
Garnish with the fresh parsley and serve.
