François Beaufort has been trying to get Google developers to add the ability to search Google Drive content from the Chrome’s Omnibox.
In the meantime, he has released a Chrome extension named OmniDrive to accomplish the same.
You can of course, manually create a search option in Chrome to search through your Google Drive.
App description:
Add support to the Omnibox to search in Google Drive.
Type “drive” in your Omnibox, pressand look for something in your Google Drive.