My guess is that if it is a hardy Kiwi which has a finer vine it should work with some training. The fuzzy ones tend to be a heavyer vine and may eventually overwhelm the fence without a lot of training and pruning.
Since kiwis are a vigorously growing twining vine, its going to be a difficult and tedious job to prune out the excess growth after it has twined itself throughout the chain link. Kiwis take a lot of summer and winter pruning to keep them within bounds and under control. Also kiwi likes to climb and even when growing on a 6 foot high trellis is continually sending new shoots 10 feet above the trellis.
Brace yourself while corporate america tries to sell us its things. Some day they will chill and use tiny ads.
Contemplate spending the next 20 years building a better world in montana