Heat olive oil in a large pot or Dutch oven over medium heat. Add ground turkey and cook, breaking it up with a spoon, until browned. Drain any excess fat.
Add chopped onion to the pot and cook until softened, about 5 minutes. Stir in minced garlic and cook for 1 minute more until fragrant.
Stir in crushed tomatoes, tomato sauce, diced green chilies, and water or broth.
Add chili powder, ground cumin, dried oregano, and cayenne pepper (if using). Season with salt and black pepper to taste.
Bring the chili to a simmer, then reduce heat to low, cover, and cook for at least 30 minutes, or up to 1 hour, stirring occasionally, to allow flavors to meld.
Serve hot with your favorite toppings.
Notes
For a spicier chili, add more cayenne pepper or a pinch of red pepper flakes.
You can prepare this chili ahead of time; flavors often improve the next day.
Store leftover chili in an airtight container in the refrigerator for up to 3-4 days.
This recipe is naturally gluten-free and can be made low-carb by omitting certain toppings.