The most common and most likely answer to this crossword clue is the 6 letter word GOATEE
I've seen this crossword clue in The Times
G
O
A
T
E
E
More clues leading to the result GOATEE
- Attack same point twice that's on chin
- Attempt at Estuary English originally – one hides one’s face a bit!
- Something worn by men in Indian state: short-sleeved shirt
- Try to meet a supporter of facial hair
- Try a support for facial hair
- It’s hairy to travel with a supporter
- Indian state supporter reveals hair on chinny-chin-chin
- Work had employees cutting off almost all facial hair
- Somewhere in India needing support — it’s hairy
- Attack ends of extensive beard
Buddy explains!

The straight part
We know that "that's on chin" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that's on chin = goatee.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 GOATEE mean?
GOATEE noun- A beard trimmed to grow only at the center of the chin.