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.
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It's like being on a deserted island - only with gardens and natural buildings in Montana