A solar chimney is not like a regular chimney and it most certainly does not work like a regular one. It is stated that it is most suitable for commercial plants and a lot of solar chimneys have already been built.
The specialty of a solar chimney is that after ambient air is drawn into a glass collector, it is warmed by a solar energy. As hot air rises in ordinary circumstances than also this cause the air to rise up in to the chimney. The rising warm air starts to drive the turbine.
Of course there is a problem that might affect the building of a solar chimney as the original capital cost are very high, but actually as the running cost are very low they are earned back. But still, building a solar chimney acquires a somewhat big first investment.
Solar chimneys are most suitable for places where a lot of sunshine is a normal part of the weather, like for example India, Australia, countries in Africa etc. There is no point of building a solar chimney in the northern parts of the world as they will not return enough energy to cover the costs of installing them.