In a large (at least 5 Quart) pot over medium high heat, add olive oil. Once the oil is heated, add the ground turkey to the pot. Cook until all of the water has evaporated from the meat and it starts to brown.
For a thicker chili, keep simmering until desired consistency is reached. For a thinner chili, you can add more water. Leftovers will be thicker and may need to be thinned out with a bit of water upon reheating.