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The Windows 8 version of Chrome responds correctly to the Windows Settings charm. Clicking that charm opens this pane, and clicking Settings here opens the familiar Chrome page on the left.
From the Windows 8 Mail app (or from People or Calendar) you can connect your Google account. Click the Settings charm and then click Accounts to see this set of options, which includes Google. (You can connect multiple Google accounts.)
After entering your Google account name and password, be sure to click the check box under it so that you can sync contacts and calendar items along with mail.