The most common and most likely answer to this crossword clue is the 11 letter word HAND-PICKED
I've seen this crossword clue in The Guardian
H
A
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D
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P
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D
More clues leading to the result HAND-PICKED
Buddy explains!

The straight part
We know that "specially chosen" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case specially chosen = hand-picked.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 HAND-PICKED mean?
HAND-PICKED adjective- Alternative form of handpicked
- To pick or harvest by hand.
- To select carefully and with individual attention.