It appears that incognito mode in the iOS 7 version of Google Chrome is broken. Searches completed in incognito windows in the updated Google Chrome app are shared with the regular browser. This is especially important as Google Chrome has a unified search and URL bar, meaning that people often search rather than typing full URLs.
This of course is a major issue for anyone who shares an iPhone or tablet with others, as it could potentially reveal sensitive or personal information about a person's browsing history. TechCrunch has reached out to Google for comment, but has not heard a reply yet. However, it's likely Google will quickly stamp this bug out and Chrome for iOS will be updated as fast as Google can get a new build through the App Store approval process. In the mean time it's best to avoid Incognito mode and keep your iOS device from anyone who should't be privy to your browser history.