My thighs are so muscular they chafe when I walk — how do I train without making them any bigger?

What are your thigh measurements? And how did they change with you performing squats? I.e. how many inches did your thighs increase? I have massive thighs and don't have that issue with them rubbing together unless I have body fat. You mentioned it is still an issue at low body fat - do you have a picture of your legs and the measurements at low body fat? That would help assess it.