Not yet, but according to Mark Zuckerberg, with an aggressive international growth strategy Facebook will be the first social network to reach the 1 billion user mark. Facebook currently has 500 million users globally, and they predict it will take less than two years to double the number of users.
Because Facebook is already the dominant social network in the western world, their strategy is to compete with established social networks in countries like China, Japan, Russia, and South Korea. Facebook has fewer than 1 million users in Russia, so there is potential for huge growth in these markets.
Will Facebook be able to beat everyone to the chase, my guess is they will… They have a huge head start. Only time will tell.