Heat oil in a large pot over medium-high heat. Sauté onion, bell pepper, chile, and garlic, stirring often, 5 to 6 minutes. Add turkey, increase heat to high, and cook, stirring often and breaking meat into chunks, until it's no longer pink, 4 to 5 minutes.
Stir in tomatoes, beans, tomato paste, chili powder, cumin, and agave. Cover and bring chili to a boil, stirring often. Reduce heat and simmer, stirring occasionally, until flavors are blended, 45 minutes to 1 hour. Stir in lime juice. If you like, add salt to taste and serve with cheese and cilantro.
Make ahead: Up to 3 days, chilled. To transport, bring to boiling and pack in a preheated thermos.
Note: Nutritional analysis is per 1 1/2-cup serving.