The only thing that causes the three point to go down, is gravity. The only thing holding it down is gravity. When the arms are at their lowest position and nothing is on them, you can lift them up freely with no resistance other than gravity.
To chain it down keeps it from raising up unless enough upward lift is generated to break the chain used. If you have tons of whatever behind you pushing on the tractor coming down a hill, there is a potential for a tail heavy trailer to use the tongue to lift up on the three point, raising the center of gravity, putting the trailer hitch at a really bad angle on the ball, and easily breaking something or causing injury.
The best method of chaining it down would be to connect a chain to the drawbar on the tractor, routed up and over both lift arms on the back of the tractor. Holding down the lift arms will prevent all of the three point from raising. I have seen people go from the drawbar to the top link and end up messing up the top link.
If you leave some slack in the chain, you can monitor it. If you ever see it raising and pulling the chain tight, you loaded the trailer too tail heavy and should load more on the front to increase the tongue weight.