Once you have a known fence jumper you have to keep him chained. I went through it for years and they'll jump any obstacle you place at the top of the privacy fence. They become driven to get out and always find your weak spot.
That is not true, I have had many fence jumpers and there are many ways to keep them contained.
How tall if your fence now? There are a few things you can do to keep him without a chain set up.
Making the fence taller
If your dog is pulling himself over the fence then the rollers work well but are really expensive
You can get an underground fence with an e collar and it will keep him a few feet from the fence so he cannot get close enough to jump it.
They also sell a radio fence where the unit lugs by your back door and you can set how far from the house your dog can go before it gets them. The underground is probably the best if you back yard is narrow.
You can build a topped dog run and line the bottom edged with paver's so they cannot dig out or jump over
You can also crate the dog if they are only getting out when you are gone.
As a trainer I have clients all the time where their big complain is they have an escape artist and it is just a matter of figuring out what works best for you. Do know that chaining is not your only option if you are not in favor of chaining them out.