Can UE4 run a an AI chess simulator?

Of course Unreal Engine 4 can be used to make Chess!

Just take quick walk over to the Documentation: https://docs.unrealengine.com/latest/INT/Search/index.html?q=chess&x=0&y=0

There’s plenty of links there to get started (I recommend checking out the TomOfNZ link; His tutorials are EXCELLENT!)