In a large pot, heat the oil over medium-high heat. Add the onion, and cook for 2 to 3 minutes until it's translucent.
Brown the meat:
Add the turkey, garlic, and seasonings and brown for 7 minutes, making sure all of the meat is cooked through and broken up into smaller pieces.
Simmer:
Stir in the tomato sauce and pumpkin puree. Bring the chili to a low boil, then reduce the heat to low and simmer for 30 minutes.
Serve:
Turn off the heat, let it sit for about 5 minutes, and serve with your favorite chili toppings.
Notes
You can use beef or ground chicken for this recipe or make it completely vegetarian by omitting the meat and adding two 15ounce cans of beans, drained and rinsed.