The most common and most likely answer to this crossword clue is the 7 letter word COFFERS
I've seen this crossword clue in The Daily Telegraph
C
O
F
F
E
R
S
More clues leading to the result COFFERS
- Charlie holds out for funds
- Reportedly people unpopular in theatre boxes?
- Chests, and people with a cold in them, say?
- Sound of heavy smokers’ chests?
- Treasury announcement for smokers?
- Funds from hundred volunteers
- Chests sounding like bronchitis sufferers?
- Chests of principally charitable things given
- Bids by Conservative for supply of funds
- Beginning to collect bids for chests
Buddy explains!

The straight part
We know that "chests" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case chests = coffers.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 COFFERS mean?
COFFERS noun- A strong chest or box used for keeping money or valuables safe.
- An ornamental sunken panel in a ceiling or dome.
- A cofferdam.
- A supply or store of money, often belonging to an organization.
- A trench dug in the bottom of a dry moat, and extending across it, to enable the besieged to defend it with raking fire.