For the chili: Place a skillet over medium-high heat and add the oil. When the oil is hot, add the ground beef and brown, crumbling as you go, until cooked through, 7 to 8 minutes. Add the garlic and tomato paste. Stir and cook for 1 minute. Add the kidney beans, tomato sauce, tomatoes and green chiles, chili powder, salt and pepper, then bring to a simmer. Continue to simmer and thicken, stirring occasionally, for 10 minutes.
For the burritos: Add about 1 cup chili to a tortilla, then top with grated Cheddar and some diced onion. Add a handful of corn chips and a dollop of sour cream. Tuck the sides of the tortilla and roll tightly, then set aside. Repeat with the remaining tortillas.
Heat a large skillet over medium heat. Add a little olive oil. In batches, toast the burritos until golden, about 1 minute per side.