Heat a large skillet over medium-high heat. Cook and stir turkey in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.
Stir tomato sauce, diced tomatoes, tomato juice, and chili seasoning mix into turkey; simmer until until chili is hot, about 5 minutes more.
Pour corn chips into a large bowl and top with turkey chili. Sprinkle Cheddar cheese over chili.