Bad news guys. Carroll, Farhi, and Guth along with 't Hooft already looked into this in the 1990s. The only way time travel is possible is if there is already a time machine in the universe. If there isn't one already, it's impossible to create one in an open universe, and in a closed universe, it's not possible to create one and then use it before the universe ends.

The proofs are in 2+1 dimensions, but they're generally believed to hold in 3+1.

http://preposterousuniverse.com/research/#ctcs for a brief summary with references by Carroll.