Heat the olive oil in a Dutch oven or large wide pot over medium-high heat. Add the turkey, 1 teaspoon salt and a few grinds of pepper and cook, breaking up any clumps with a wooden spoon, until brown, about 8 minutes. Remove the turkey and set aside. Add the garlic, celery, onion and 1/4 teaspoon salt to the pot and cook, stirring occasionally, until the vegetables have softened, about 8 minutes. Add the chile powder and tomato paste and cook, stirring, 1 minute.
Return the turkey to the pot and add the diced tomatoes, beans, green chiles and chicken broth. Increase the heat to medium-high and bring to a simmer, then reduce the heat and simmer until the vegetables are tender and the flavors have melded, about 30 minutes.
Serve the chili topped with the cheese, sour cream and scallions.