Preheat oven to 400°F. Brush squash cut sides with 1 tbsp oil, season, and roast cut-side down 35–40 minutes until strands separate with a fork.
While squash roasts, heat remaining oil in a skillet over medium-high. Sear chicken pieces until golden and cooked through, about 6–8 minutes. Remove and set aside.
In same skillet, sauté onion until soft, add garlic and tomatoes, cook 2 minutes. Stir in olives, oregano, and chicken to warm through.
Scrape squash strands into the skillet, tossing to combine with the chicken mixture. Fold in feta and parsley, adjust salt and pepper, and serve warm.