Chewing Lunge Line

I have been doing some in hand work with my 3 year old (just 3) and he is being fine - except that he does like to grab hold of the lunge line (just a short one) and hold it in his mouth, not even chewing it all the time. We are only walking round the school, changing direction, halting, a little bit of trotting, nothing difficult. But he is like a baby, wants his dummy in his mouth. He doesnt do it when I am leading him from field to stable.

Anyone had any experience of this? Is it just a bit of insecurity which he will get over in time? I am thinking of putting a bit on him, just to give him something "proper" to hold on to. Would appreciate views from the experts here!

Thanks
Jay