Preheat oven to 425°F (220°C). Toss squash halves with 1 tbsp olive oil, salt, and pepper; place cut-side down on a baking sheet.
Whisk maple, Dijon, vinegar, remaining oil, thyme, garlic, salt, and pepper in a bowl.
Pat chicken dry, season, and brush or spoon half the glaze over thighs.
Roast squash for 25 minutes; add chicken to the sheet, skin-side up, and roast another 25–30 minutes until chicken reaches 165°F and squash is tender.
Brush remaining glaze on chicken during the last 5 minutes. Scrape squash with a fork into strands; serve with chicken and parsley.