Hawking seems to agree with the two premises and the conclusion of the Kalam cosmological argument - Whatever begins to exist has a cause; the universe had a beginning; therefore the universe has a cause. However, he posits gravity as the cause. It seems to me that Hawking is making a pretty big blunder here - he says that we have the law of gravity so it's inevitable that the universe would create itself - does he really believe the law of gravity existed before the universe? If so, how? He takes something true of the universe and then says it was used to create the universe. What does it really mean that the law of gravity existed before anything else? The law of gravity is simply a description of what happens in our universe - it doesn't actually cause anything, but even if it did - what exactly did the law of gravity operate on to bring the universe into existence when there was nothing? The matter wasn't in existence?
Additionally, isn't it lucky that the force of gravity was what it was (along with the other nearly 100 finely tuned constants) or life in the universe couldn't exist.
Finally, if an event is the effect of an impersonal cause then the effect will be as old as the cause, and on Hawking's view that would mean that the universe is as old as the law of gravity, i.e. eternal, but he knows that the universe came into existence a finite time ago. That means the cause must be personal, and He chose to act in creation.
Many atheists will take comfort and encouragement in Hawking's declaration of unbelief, but it requires them having a great deal of blind faith - more faith than I could muster.
In the beginning God created...
See also Professor John Lennox's article.