Everything you search for on Google is kept for 18 months (and every other search engine does the same for legal reasons). I personally like the feature, and since I don't use Chrome to view any thing internally, I don't see any privacy issues with this specific feature.
But in this case, I seriously doubt many people here have ever stopped and thought for a second before they search for something Google. @bounty, how much of that porn collection was found using Google? the actual search results to find said porn would be more embarrassing than searching for an internal system someone outside your LAN couldn't access.
I doubt any of you think of the ramifications of what you search Google, so why do you care if they (or any other search provider of your choice) get a few word and sentence fragments more?