Fact: the particle collider near Chicago (Fermilab) has been running an antimatter beam for the last 10 years.  Millions of times a second it crashes into a matter beam going in the opposite direction and exotic forms of matter are produced.

Fact: high energy collisions like this (and even much much more energetic ones--much higher in energy than what will happen at the LHC) occur all the time when cosmic rays from outer space hit dust particles in our upper atmosphere.  Again, particles are created, and the ones that don't decay in flight are going through us every second.