Answer: Apple trees on a dwarfing or semi dwarfing rootstock can be trained to grow that way (or in a variety of shapes) through an age old selective pruning and training method called espalier. This is not terribly difficult to do but training needs to begin from the start and it requires several years to establish the branch pattern framework and then you must continue to prune according to the pattern to maintain it. With apples, since you would be pruning annually anyway, this is not really extra work. In fact, apples are a good choice for this technique since they withstand pruning so well.
The following web page
includes instructions for training along wires. These could easily be adapted for use along a chain link fence. Many good pruning books will also include a section on espalier with diagrams or illustrations.
Good luck with your project!
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