Way back when (like about 1975, before even my time
) the US Forest Service began requiring climbing helmets for its climbers, chin strap use was specifically mandated as well. The reasoning then, and it makes sense to me still, was that a fall in a tree would be likely to mean the climber could strike multiple limbs on the way, so the idea was to keep that helmet firmly in place even when it takes several knocks in succession. I don't think muffs would suffice in that instance. Besides, if I'm not actually running a saw, I push the muffs up on the helmet, so I can hear and communicate. Then the helmet is definitely loose without the strap.
If the only thing one is wanting to protect their noggin from is a falling piece of tree hitting them, I take Mick's point. But for full potential benefit of the ppe, using the chin strap is smart.