Cryptic crossword clue
Chat-up line is one primarily about essential oil 9

The most common and most likely answer to this crossword clue is the 9 letter word PATCHOULI

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "essential oil" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case essential oil = patchouli.
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 PATCHOULI mean?

PATCHOULI noun
  1. Any of several East Indian plants in the genus Pogostemon, especially Pogostemon cablin, which yield a highly fragrant oil.
  2. The oil or perfume made from these plants.

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