The most common and most likely answer to this crossword clue is the 6 letter word GROUCH
G
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H
Buddy explains!

The straight part
We know that "Chronic complainer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case chronic complainer = grouch.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 GROUCH mean?
GROUCH noun- A complaint, a grumble, a fit of ill-humor.
- One who is grumpy or irritable.
- To be grumpy or irritable; to complain.