Heat olive oil in a large soup pot over medium heat; brown turkey, stirring often, until crumbly and no longer, pink, about 10 minutes.
Drain and discard any fat.
Transfer turkey to a slow cooker and stir in diced tomatoes, pumpkin, chili beans, black beans, brown sugar, pumpkin pie spice, and chili powder. Set cooker to Low, cover, and cook until pumpkin is tender and has started to break apart, at least 3 hours.
