Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
Slice each chicken breast lengthwise to make thinner cutlets, then place the pieces on the prepared baking sheet in a single layer.
In a small mixing bowl, stir together the mayonnaise, shredded cheddar, and BBQ sauce until evenly combined.
Spread the mayo–cheddar–BBQ mixture evenly over the top of each chicken piece.
Sprinkle the plain breadcrumbs evenly over the coated chicken pieces.
Bake for 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and is cooked through.