Depends. The classicle leasons of chickenpox are superficial & generally leave transient marks that fade over a year or so.However, if a kid scratches & digs at leasons there is a chance that a deeper wound will appear and scar. There is also risk that weeping sores will be invaded by staph or strep and cause even bigger problems. Simple surveylance and cleaning of wounds can minimize risk.
Scarring. Some lesions may leave scars, especially if they are scratched and get a secondary infection. Also, some people scar more easily than others.