In the 1400s and 1500s this was a relatively common spelling of chimney in the West Riding although I have found no reference to its use in major dictionaries.
These words may have the same meaning: initially they referred to split oak boards which were imported from the Baltic and used by coopers for barrel-staves.
To cleave wood was to split it along the grain, using iron wedges and a heavy hammer: ‘cleft’ and its variants referred to pieces of cleft wood or board.