I would agree with Lid that Tom Wijsman's solution was not what fixed it for me. Lid's solution was closer, and one that I have tried several times but still could not get to work. I understand OP was looking to remove specific suggestions, but if you were in the same situation as I was (where I was unable to remove anything like that), the following should help you out.

I tried the keyboard shortcut deletes Tom Wijsman describes, clearing my entire history (since "Beginning of Time"), disabling syncing (in case the entries were stored in the cloud), disabling Omnibox History and Autofill specifically from syncing, clearing my synced data, uninstalling and reinstalling Chrome, and removing the History Provider Cache. None of these were removing the suggestions Chrome would give me based off my past brow

Instead of removing the History Provider Cache file, I actually had to remove the History file.

It's in the same path (Mac OS X /Library/Application Support/Google/Chrome/Default/ and on Windows I would assume C:\Users{username}\AppData\Local\Google\Chrome\User Data\Default as stated before).

I'm not sure why this was not being cleared out with the regular Chrome history clear. I noticed the file was 9.3MB.