Since the Galaxy Tab runs Android OS, I'm taking your question to be whether or not Chromium will run on Android.
My answer is no, not as of yet.
That being said, however, the browser that comes built-in with Android is essentially Chrome optimized for mobile platforms (such as cellphones and tablets). Chrome/Chromium and the Android web browser share code
For more discussion of this topic check out http://www.redmondpie.com/google-wor...d-may-be-next/
If you're looking for an alternative to the built-in browser, the linked page above recommends "Firefox for Android, Opera Mobile and the surprisingly powerful Dolphin Browser HD – all of which can be found on Android Market."