The most common and most likely answer to this crossword clue is the 5 plus 5 plus 5 letter word CERNE ABBAS GIANT
I've seen this crossword clue in Financial Times
C
E
R
N
E
A
B
B
A
S
G
I
A
N
T
More clues leading to the result CERNE ABBAS GIANT
Buddy explains!
The straight part
We know that "He’s chalked up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case he’s chalked up = cerne abbas giant.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.