I'm a bit behind the times on this one, but it's a cool story that deserves a post. Here's the punchline: according to a December 2011 paper in the journal "Thinking & Reasoning", you're at your most creative when you're groggy and out of it. In the study, Mareike Wieth (Albion College) and Rose Zacks (Michigan State) recruited 428 undergrads and used a questionaire to identify them as either night owls or morning larks. They then gave the students a set of problem-solving tasks, half of which required creative insight and the other half of which were narrow-focus analytical questions. Some of the students were given the test first thing in the morning, and the others were tested in the late afternoon.
Their big finding was that students were much more successful at solving the insight problems when tested at their least optimal time of functioning. When tested "off-peak" (night owls in the morning and vice versa) the students averaged success rates of 56%, 22%, and 49% for the three insight tasks, versus 51%, 16%, and 31% when tested at their preferred time of day. In contrast, the performance on analytical questions was unaffected by time of day.
The explanation is that insight-based problem solving (creativity!) requires a broad, unfocused approach, which is easier when your inhibitory brain processes are weaker and your thoughts are meandering.