Can you move child out of state if no custody is in place?

My cousin wants to move to Texas with her 4 yr old boy to be with her family because grandma is too old to help out. My cousin and her ex do not have a custody agreement. Only this he is supposed to be paying child support but she's only gotten 3 payments these 4 yrs. We live in Chicago...Can she move? the ex told her "No, stay here and struggle while I laugh at you" but he fails to realize the only one hurting from this is the kid.