Winding him up

In Brooklyn and other places in the NYC area it is customary to refer to giving someone a hard time as "busting his chops". I've also heard it used to indicate teasing "Hey, I'm just busting your chops".

Anyway, I'm wondering where it comes from and especially what the "chops" are. Any ideas?

That'll teach me to ask questions before my morning coffee!

Is the British equivalent "winding him up"? Or is that kidding someone?

'Kidding' is a pretty good way of describing 'winding up'. However, 'to wind up' sombody can be quite deliberately nasty with the object of getting the person to lose their temper. It seems a perverse pass time, but people do it.