I am not sure if they would destroy the old chain link fence, more like swallow it. The weight of the shrub may be an issue, especially when wet, but if the chain link fence is in good condition, I would try it. The rootlets like attaching to rough surfaces.

Hi Luis - They will actually be growing on the new wood fence, not the old chain link. The wood fence will be right up against the chain link one (which still in very good shape). I'm hoping that the two fences together will be strong enough to support the climbing hydrangeas - at least until they grow into monsters.

When growing them on the chain link I had to keep interweaving the branches. On their own they would just grow straight out, and were not too happy without anything to attach their rootlets to. After about three years they weren't yet swallowing the chain link, but they were starting to cover it well.

Your climbing hydrangea will attach quite firmly to your wood fence and is not likely to ever get heavy enough to collapse the fence. Be sure to build the fence to last a long time and not have to replaced when your hydrangea is finely at its best. Al