From RockClimbingTipsWiki

[edit] Chimneys

There are a lot of ways to ascend chimneys, but here are some suggestions. These all assume that you have no decent hand- or footholds, but the walls have quite a lot of friction.

Start here.

The next step is to move one foot to the wall behind you.

Stand up with one foot on each wall, and press your arms against the wall to lift your body upwards without dragging it. This is probably the most comfortable part of the cycle to take a rest if needed!

Move that leg from behind you up to the wall in front of your waist...

... and then move up the lower leg to complete the sequence.

Of course the chimney could be wider or narrower than the 'standard' one! In the latter case the technique is easy to adapt but wide chimneys can be hard work for the arms.

In the case of the wide chimney, don't forget that there might be handholds around on the back wall which you haven't noticed. An easier approach might be this one, which takes most of the body weight on the legs whilst using handholds on the back wall to as well: