Preheat the oven to 200 degrees . Wrap the tortillas in foil and place in the oven.
In a nonstick skillet, heat the olive oil over medium heat. Season the chicken with salt and pepper and place in the pan; cover loosely with foil and cook, turning once, until golden and cooked through, about 12 minutes; transfer to a plate. Brush the chicken on both sides with the hot sauce and tent with foil to keep warm.
Meanwhile, using a food processor, blend the blue cheese, mayonnaise and 2 tablespoons water until smooth; transfer to a large bowl. Add the lettuce, radishes and carrots and toss to coat.
Thinly slice the chicken against the grain. Lay the tortillas on a work surface in a single layer. Divide the salad among them; top with the chicken and any juices.