It should be there right?
Ubuntu 13.10 - 64Bit
This question appears to be off-topic. The users who voted to close gave this specific reason:
It should be available in the Ubuntu Software Center, yes. If you search for:
you should have results including the Chromium Web Browser and Chromium BSU, an arcade game.
You should also be able to install by clicking on this button:
If Chromium Web Browser isn't showing up in the Software Center results, it may be because 13.10 is still in beta.