The most common and most likely answer to this crossword clue is the 8 letter word WISHBONE
I've seen this crossword clue in The Times
W
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S
H
B
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More clues leading to the result WISHBONE
- Part of chicken new bishop mostly cooked?
- ,24 Possibly a Christmas cracker to pull thus contains letters on a pencil in red, say?
- Its majority shareholder can ask for anything, supposedly
- Part of the chicken's offensive formation
- Whine and sob terribly — can this bring luck to one of couple?
- Sensible to capture pencil marking on part of avian skeleton
Buddy explains!

The straight part
We know that "Part of chicken" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of chicken = wishbone.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WISHBONE mean?
WISHBONE noun- A forked bone between the neck and breast of a bird consisting chiefly of the two clavicles fused at their median or lower end, regarded as a lucky charm in some countries.
- A spar in two parts, between which a sail is hoisted, the wishbone extending its clew.
- Any sailing vessel rigged with a wishbone.
- A particular kind of offensive formation. See wishbone formation.