Answer: It sounds as though you can train a vine up the chimney. If so, here are a few suggestions:
Honeysuckle (Lonicera) need support when they are first starting out, but are generally profuse bloomers. Hardiness and flowering vary greatly with the variety you choose. Great for hummingbirds.
Trumpet vine (Distictus buccinatoria) flowers best in full sun but will bloom in partial shade. It is hardy to 24 degrees F.and needs yearly pruning to keep it under control. It blooms sporadically with warming weather.
Virgin's Bower (Clematis paniculata) is very hardy climber from the Orient that will reach 30 feet. White, fragrant flowers in August and September.
Dutchman's Pipe (Aristolochia littoralis) has a very unique 'calico' flower and is evergreen and hardy to 25 degrees F and root hardy to below 20 degrees F.
'Mme. Galen' Trumpet Creeper (Campsis x tagliabuana) has bright orange flowers and is hardy to below 0?F.
You might also consider climbing hydrangea. Hydrangea anomala petiolaris is one of the best of the ornamental vines and useful because it will grow and flower even in a northern exposure. This is a large heavy vine that requires a very sturdy support. Reddish brown, peeling bark is attractive in the winter. This plant starts out slow, but can become a vigorous grower in 3-4 years. Plan to prune it back annually so it won't overtake the area.
If vines aren't what you had in mind, how about planting columnar evergreens such as Arborvitae? These maintain a 2-3' width and grow upright to 15 feet.
Hope one of these suggestions appeals to you!
Q&A Library Searching Tips