Yes; it's called Midnight Sun. From Wikipedia:
Midnight Sun is an unreleased companion novel to the book Twilight by author Stephenie Meyer. The work retells the events of Twilight, but is written from the perspective of Edward Cullen instead of that of the series' usual narrating character Bella Swan. Meyer stated that Twilight was to be the only book from the series that she planned to rewrite from Edward's perspective.
It was leaked on the internet prior to completion, which pissed Meyer off so much that she didn't finish writing it:
On August 28, 2008, Meyer halted the writing of Midnight Sun in response to the leak of twelve chapters of the unfinished manuscript on the Internet. She stated, "If I tried to write Midnight Sun now, in my current frame of mind, James would probably win and all the Cullens would die, which wouldn't dovetail too well with the original story. In any case, I feel too sad about what has happened to continue working on Midnight Sun, and so it is on hold indefinitely." She made the twelve-chaptered draft available on her website in fairness to her readers, now that the novel has been compromised before its intended publication date. Meyer also stated that she doesn't believe the manuscript was leaked with any malicious intent, and would not give any names.
Update five years later: Midnight Sun was published on 4 August 2020.
