Yes, a stud chain. They are referred to as 'lead shanks' also. In halter & showmanship, depending on where you are showing they are a requirement. I, personally like a lead with a short chain that can just be doubled over in the ring under the halter and neither used over or under. If it has to be used (I've seen some places that it is a requirement that it be over/under in an in hand class - don't agree with it but it is what it is), I don't like seeing them under because if they actually have to be used, the horse's typical reaction is to get away from the pressure and with it under getting away means going up.
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.