A singularly unwell American playwright (6)

I believe the answer is:

oneill

I'm a little stuck... Click here to teach me more about this clue!

'american playwright' is the definition.
'O'Neill' can be an answer for 'playwright' (Eugene O'Neill, American playwright 1888-1953). I'm unsure of the 'american' bit.

'a singularly unwell' is the wordplay.
'a' becomes 'one'.
'singularly unwell' becomes 'ill' (similar in meaning. I am not sure about the 'singularly' bit.).
'one'+'ill'='ONEILL'

Can you help me to learn more?

(Other definitions for oneill that I've seen before include "American dramatist" , "Eugene -, US playwright (The Iceman Cometh)" , "Eugene ..., Tip..., Ryan ... (1'5)" , "Eugene --, US dramatist" .)

I've seen this clue in The Guardian and The Globe and Mail.

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