Heat oil in a frypan on a medium-high heat. Pat chicken dry. Add to pan with a pinch of salt and cook for 6-8 minutes, tossing occasionally, until golden and cooked through.
Grate carrot and roughly chop lettuce. Add to a medium bowl, along with chicken and dressing and toss to combine. Season with salt and pepper.
Divide filling evenly between wraps, fold tightly and enjoy.