im pretty sure those chains are very strong under normal use, have you put a lot of strain on it in 4 wheel, or someone before you? the chain could be stretched, or it could be something in the front end and not even the transfer case at all.
first thing i would do would be check the fluid in the case, just unscrew the top plug, on level ground fluid should be just even with that hole. stick your finger in it, should be fairly clear, like clean oil. if it feels and looks ok but is low, add someone, it will say in your owners manual ( i think it might be 75-90w gear oil, but dont trust me on that)
if it feels and looks bad drain it through the bottom hole, reinstall plug and fill untill level with top plug. you may need a gear oil pump to succesfully complete this