The first plant that came to my mind is the Montana Clematis...or any other Clematis for that matter.

I found this article on the web....maybe you might get some ideas:

Plants suitable to hide a wall -

Firstly, decide which way the wall in question is facing as this is imperative to know when selecting the most suitable plant.

North facing walls - the ground in front of a north facing wall will suffer from dampness and lack of sunshine. Some suitable varieties could be Clematis hybrids, climbing Hydrangea, Ivy, winter Jasmine or Roses (e.g. 'Gloire de Dijon', 'Mme Alfred Carrière' and 'Mme Grégoire Staechelin').

South facing walls - as these get plenty of warmth and sunshine dry soil could be a problem. Try Honeysuckle, Passion Flower or annual climbers mentioned above, such as Nasturtium and Morning Glory or Ceanothus, Mexican Orange or Myrtle which are more tender plants.

East facing walls lack sunshine and sometimes suffer from cold winds. Flowering Quince and Forsythia should be suitable and most Roses would be O.K.

West facing walls are probably the best site of all and, therefore, decorative shrubs and climbers such as Magnolias, Camellias, Wisteria, Honeysuckle or Clematis Montana would be ideal.

Happy Planting,

Annie

It covers the chain link fence for more privacy. Full coverage even in winter.
Then you can always plant other
taller things in from of it, blooming shrubs
Hibiscus, forsyntha's, lilac's, rose of sharon's, rhododendrum's, etc. And/or tall perennials like hollyhock's, delphiniums, lillies, etc. and plant medium to small perennials and annuals in between.

Or if you just want to plant a plant, try some type of climbing vines, perennials would be a clematis, climbing roses, Japanese honeysuckle (I think that's the non~evasive one) or if your fence is heavy duty could be wisteria. And/or annuals such as morning glories or cardinal climbers, sweet peas (annual and perennials), or nastrutiums.