There are many commercial manufacturers of what are called "privacy slats" or "privacy strips". These are plastic or vinyl strips that are woven between the links of the chain link fence, either vertically or in a diagonal orientation. They serve to reduce the amount of light that passes through your fence, and can turn a traditional chain link fence in to a serviceable privacy fence.
Commercial chain link fence fabric suppliers manufacture materials that can be wired to an existing chain link fence and afford some level of privacy to your yard. These materials are often nylon or canvas in construction, and can last for many years.
A chain link fence can be used as a trellis for growing vines, such as grapes, or climbing plants such as any of the climbing rose cultivars. This can afford your yard a level of privacy at very little cost. Additionally, vines and plants can be pruned or allowed to fill out to reduce or increase the level of privacy in your yard. One issue with this method, however, is that climbing plants and vines are typically deciduous and thus will leave your yard decidedly un-private throughout the winter.
If cost is an issue, and you are opting for function over form, a simple plastic tarp zip-tied to your fence can turn a see-through chain link installation into a privacy fence. Tarps come in a variety of colors, and are available in most any home improvement store, so you can complement your fence color by using a similar colored tarp. It may not be the prettiest fence on the block, but it will get the job done.