It was kind of both, depending on the timeline. Early on it was word of mouth, then Google saw they had momentum and they capitalized on it with the banners and aggressive marketing.
So many replies in this sub thread opining authoritatively. Share your source. Did you have access to the data on Chrome's user growth and which marketing campaigns were the sources of which users?
From my perspective, all of you are saying a lot of things as if you know them to be true, but you have no idea whether they're true or not; really, you just find them to be plausible.