I've seen his use of this particular phrase quoted by many in their obituaries. In very, very few places--five found by Google, just now--is the phrase attributed to Edna St. Vincent Millay.
"My candle burns at both ends
It will not last the night;
But ah, my foes, and oh, my friends -
It gives a lovely light."
- Edna St. Vincent Millay, "A Few Figs from Thistles"
It's a perfect quote for the situation, and I'm sure Hitchens knew who he was quoting.
Is this such a commonly known quote that everyone knows where it came from? Or has the "candle burning at both ends/giving a lovely light" simply become a common saying that everyone knows, so attribution is unnecessary? Or is it just that my Google-fu is awful?
(I'm a terrible judge of how common it is because my first serious girlfriend wrote her thesis on the works of Edna St. Vincent Millay.)
*First half of quote at 0:45, second half at 2:20. Transcript at: http://transcripts.cnn.com/TRANSCRIPTS/1112/16/acd.01.html. Non-embeddable video at: http://www.youtube.com/watch?v=zeiS7hYbb8c