Chimney-cleaners win the lottery (10)
I believe the answer is:
sweepstake
'the lottery' is the definition.
(sweepstake is a kind of lottery)
'chimney-cleaners win' is the wordplay.
'chimney cleaners' becomes 'sweeps' (I've seen this in another clue).
'win' becomes 'take' (taking is a kind of winning).
'sweeps'+'take'='SWEEPSTAKE'
(Other definitions for sweepstake that I've seen before include "gamble" , "System of gambling, especially on horse races" , "Lottery" , "lots here" , "I'd bet on it" .)