The most common and most likely answer to this crossword clue is the 10 letter word PLATITUDES
I've seen this crossword clue in The Guardian
P
L
A
T
I
T
U
D
E
S
Buddy explains!

The straight part
We know that "chestnuts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case chestnuts = platitudes.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 PLATITUDES mean?
PLATITUDES noun- An often-quoted saying that is supposed to be meaningful but has become unoriginal or hackneyed through overuse; a cliché.
- A claim that is trivially true, to the point of being uninteresting.
- Flatness.
- Unoriginality; triteness.