A slow consistent curl in a chimney is a common observation in an old chimney constructed with lime mortar.
This phenomenon appears to be the result of two actions.
Over time, the mortar joints on one side of the chimney are absorbing and retaining water which freezes and expands the mortar breaking the composition of the mortar and the bond of the mortar to the brick. On the opposite side of the chimney, the mortar may be actually washing out of the joints. The chimney is getting taller on one side and possibly shorter on the other side. Hence, the curl.