The most common and most likely answer to this crossword clue is the 9 letter word MULTITASK
I've seen this crossword clue in Financial Times
M
U
L
T
I
T
A
S
K
Buddy explains!
The straight part
We know that "work while doing other chores?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case work while doing other chores? = multitask.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 MULTITASK mean?
MULTITASK verb- To schedule and execute multiple tasks (program) simultaneously; control being passed from one to the other using interrupts.
- (of a person) To handle multiple tasks at once.