As luck would have it (2,6)
(Other definitions for by chance that I've seen before include "Unplanned, as it happened" , "Fortuitously" , "As it happened, without being planned" , "Without advance planning" , "unwittingly" .)
'as luck would have it' is the definition.
(synonyms)
This is the entire clue.
(Other definitions for fortunately that I've seen before include "Luckily" , "As luck would have it" , "By good luck" .)