Chip away at (5)
I believe the answer is:
erode
'chip away at' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for erode that I've seen before include "'Deteriorate, wear away (5)'" , "Grind down" , "Become ground down or deteriorate" , "Wear away with weather" , "Gradually destroy" .)