Cook onion in oil in a large frying pan over medium heat, stirring often, until golden, 12 to 15 minutes. Add chopped thyme, salt, and pepper and cook another minute. Let cool. Stir in yogurt and transfer to a bowl. Chill at least 30 minutes (it's even better the next day). Garnish with thyme sprigs and serve with chips.
Make ahead: Up to 4 days, chilled.
Note: Nutritional analysis is per 3-Tbsp. serving.