[The Scientist (OP)]

Any architect will tell you that chimneys are never used as a weight-bearing part of a wall. Why is that so?

[Bored chemist]

What holds up the chimney pot?

[SeanB]

As they get very hot during use, and thus expand and contract, they will quickly break away from any masonry that they are holding up, and leave it unsupported. As well the chimney is the one part of the house that is likely to be broken down and rebuilt during the life of the house, as you do need to reline it due to the bricks wearing out.

[Murchie85]

I used to be a brick layer and as I recall the chimney is not made from normal common brick or facing bring, it is usually fire or engineering brick and hence not designed to be massively load baring. Fire bricks can be quite brittle and smash easy so I don't think the would be good under huge amounts of strain, also there is the issue of the expansion and contraction of the brick.