Spread the tortilla chips in an even layer on a large serving platter or baking sheet.
Drain the kidney beans thoroughly.
In a bowl, mash the beans with a fork or potato masher to your desired consistency. For a smoother texture, purée them in a food processor.
Heat the vegetable oil in a small frying pan over medium heat.
Add the mashed kidney beans and cook, stirring constantly, until warmed through.
Remove the pan from the heat and stir in the Greek yogurt until the mixture is smooth and creamy.
Carefully spoon the warm bean mixture evenly over the bed of tortilla chips.
Immediately sprinkle the grated Cheddar cheese over the top and serve.