UPDATE March 12, 2013: Google has released an update to Chrome for iOS to fix the startup crash through the App Store.
Google recently released Chrome version 25 for the iPhone and iPad, and as great as the new features might be, many users are reporting that the app crashes on start up. I am one of these
users, but I think I found a fix for the issue, which seems to revolve around the syncing protocol, specifically Google anonymous data collection. In order to do this though, you must be quick.
1: Uninstall Chrome for iOS by holding down the icon on the home screen until the icon start to jiggle. Then click on the little x in the top left corner of the app.
2: Reinstall the app from Apple’s App Store.
3: Open the app and hit check “Send Anonymous Usage Data”. Many users in the comments are saying that they had to accept Google’s “Anonymous Usage Data” option on the Terms of Service page in order to get this to work. I did not have to do this on my end, but so far it seems I am the exception. Click “Accept and Continue” when the Terms of Service pop up.
4. When the Google sign-in screen pops up, hit skip.
This is how I got the app to work for me. I had tried just the reinstall, but that still crashed the app for me. It was only when I skipped the login screen that I could once again use Chrome for iOS. I can also confirm that I was afterwards able to re-login to my Google Account and begin syncing Chrome again as normal.
It is interesting to note the the majority of those of people having this problem, though certainly not all, are users using a jailbroken device. Whether or not this is an issue with the jailbreak, with Chrome, or with both has yet to be seen. It has also been verified that Cydia apps/tweaks like BrowserChooser seem to be having no effect in either causing or eliminating the crashes.
Let me know if this worked for you or if you have any other methods that worked. And please share this so we can help others. Hopefully this issue will be resolved soon.