Where is Chrome for iOS?

It wouldn’t take much to set it apart. Just a few key features that Mobile Safari lacks:

• Wireless syncing of passwords and bookmarks with Chrome desktop through your Google account.
• Push notifications that integrated with Google’s services (like Gmail and Calendar). These would open the right URL in the browser.
• A single field for search and URLs, just like on the desktop

This wouldn’t have any problems from a code point of view, at least that I can see. They would have to use Apple’s built in Webkit rendering and Javascript interpreter (no V8), but Google don’t seem to be purists about this sort of thing.

It would allow Google to compete with one (or three, if you consider Mail and Calendar) of Apple’s built-in applications on their home turf and provide a better iPhone experience for Google’s apps - assuming Apple would ever let it through the app store. 

It would also give them a foothold on their biggest competing mobile platform in a way that Apple couldn’t really do on Android.