Heat a little of the oil in a pan over medium-high heat. Add the chicken breast, skin-side down, and cook for about 6 minutes until crisp and brown. Turn and cook on the reverse side for about 5 minutes, or until the chicken is cooked through. Leave to rest for 5 minutes. Slice.
In the meantime, add the remaining oil, mayonnaise, mustard, garlic, and vinegar to a jam jar. Season with salt and pepper, put the lid on and shake to make a Caesar dressing.
Mix the lettuce with the tomatoes and parmesan. Add the dressing and toss to coat.
Heat the tortillas in a microwave or a hot dry pan. Add the salad, followed by the sliced chicken, roll up into wraps and serve warm.