Chimney cleaner's earnings are a bit if a lottery (10)
I believe the answer is:
sweepstake
'a lottery' is the definition.
(sweepstake is a kind of lottery)
'chimney cleaner's earnings' is the wordplay.
'chimney cleaner' becomes 'sweep' (I've seen this before).
'earnings' becomes 'stake'.
'sweep'+'stake'='SWEEPSTAKE'
'are a bit if' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Other definitions for sweepstake that I've seen before include "action on race" , "System of gambling, especially on horse races" , "I'd bet on it" , "gamble" , "Lottery" .)