Special place to bury Chip (8)
I believe the answer is:
splinter
'chip' is the definition.
('splinter' can be a synonym of 'chip')
'special place to bury' is the wordplay.
'special' becomes 's' (common abbreviation as in Special Air Service).
'place' becomes 'pl' (I've seen this in other clues).
'to bury' becomes 'inter' ('inter' can be a synonym of 'bury').
's'+'pl'+'inter'='SPLINTER'
(Other definitions for splinter that I've seen before include "Thin sharp piece of wood or glass" , "Element in diamond" , "Shard" , "Thin needle-like piece" , "Rent slip? (anag)" .)