Preheat oven to 400°F. Halve the squash, scoop seeds, drizzle 1 tbsp oil, season with salt and roast cut-side down 35–40 minutes until tender.
Meanwhile whisk lemon zest, juice, 1 tbsp oil, oregano, garlic, salt, and pepper. Marinate chicken 10–15 minutes if you have time.
Sear chicken in a hot skillet 4–6 minutes per side until cooked through, or roast 20–25 minutes at 400°F.
Shred squash with a fork into strands and toss with a little olive oil and a pinch of salt.
Slice chicken, toss with squash, sprinkle feta, parsley, and olives. Serve warm.