Question about jumping fences.

Is there anything I can do to discourage my Goliath from jumping fences?

He has been neutered and goes on long walks twice daily... but if left outside for longer than twenty minutes or so he hops over a seven foot privacy fence.

I cannot chain him outside for even a short period due to being in Texas heat and he was a rescue situation where he was left on a chain to starve so it would obviously terrify him. Not to mention I don't think any dog should be chained. I would love for him to be able to be outside to play more but unless someone is watching him he goes right over the fence. That is even with his playmate Lilly out there who is to chicken to follow him.

It's like he takes himself off on a walk and then returns home about half an hour later. Almost like patrolling the neighborhood between his normal walks if that helps explain it at all?