Chrome (or Chromium, if you prefer to have someone else run your builds) is open source. It's subject to inspection. It's got some known privacy issues (e.g., safe-browsing mode sends a file URL and hash which is stored with your IP for two weeks, then your IP is stripped).
But if there's anything really untoward going on and people learn about it, it's going to look extremely bad for Google.
While I wouldn't say that's impossible, it's not a high-likelihood event in my book.
Of course, you're free to use alternative browsers.
Just ... keep in mind that if you're using a WebKit browser you're trusting Apple, and if it's WebCore, you're still trusting Google.
Most of which can be addressed. There's also a UUID in each build. Privoxy can remove that AFAIU. I don't use Chrome myself, but Chromium.
As I said: you're arguing in the absence of evidence on a pretty widely available and analyzed application. Rather than simply throwing out hypotheticals, a more interesting exercise would be to do some research of posted information to see if there are known issues. Might even make for an interesting HN submission.
Install Firefox instead.