Yes this could cause a crash on a fixed gear. If your chain gets so loose that it can fall off, it can wrap itself around your cog and bad things happen. Your wheel can lockup, and you will almost certainly mess up the paint on your new bike.

You should get this fixed if there is a large difference in chain tension. If you are setting the chain so tight that it binds, you will wear out everything much faster. First try repositioning the chainring as mentioned Sheldon's link. If that doesn't work you probably need a new chainring.

If you bought this bike from a shop, take it back and have them fix it. It is completely unacceptable for a brand new bike to be sold like this from a shop. If you bought it online or something, you will have to fix it yourself.