Cryptic crossword clue
That chap's greeting Mike 3

The most common and most likely answer to this crossword clue is the 3 letter word HIM

I've seen this crossword clue in The Times
H
I
M

Buddy explains!

The straight part
We know that "That chap" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that chap = him.
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 HIM mean?

HIM pronoun
  1. Honorific alternative letter-case form of him, sometimes used when referring to God or another important figure who is understood from context.
HIM noun
  1. A male person.
HIM pronoun
  1. A masculine pronoun; he as a grammatical object.
  2. Used reflexively: (to) himself.
  3. With nominative effect: he, especially as a predicate after be, or following a preposition.

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