The Recently Closed link that appears on Google Chrome's New Tab screen is closely linked to your browsing history. It shows tabs that you have shut down during the current browsing session and previous sessions, and while there is no way to switch off the Recently Closed tabs feature you can clear the list by removing some or all of your browsing history. How much of your browsing history you will need to wipe will depend on the duration of your current browser session and the number of tabs you've shut down.
Open the Chrome menu and choose "Settings" from the list.
Click "Show advanced settings" and then the "Clear browsing data" button.
Choose a period of time to erase from the drop-down list, from "the past hour" to "the beginning of time." How far back you need to go depends on the date of the entries in the Recently Closed tabs list.
Tick the box marked "Clear browsing history" and select "Clear browsing data." Once the data has been wiped (this may take some time if you are clearing months or years of history) open up a new tab within Chrome. If you have erased all of the entries in the Recently Closed tabs list it will no longer appear.
The Recently Closed tabs list remembers up to 10 recently closed tabs. If you shut down Chrome with multiple tabs open, these tabs are grouped together as one entry. The list is saved between browser sessions and is not affected by restarting your computer.
The Recently Closed tabs list is linked specifically to your Chrome user account, if you have one activated. If you want to keep your browsing history private you can create multiple user accounts from the Chrome Settings page, but these profiles are not password protected and can be easily switched.
Google Chrome does not save your browsing history when run in Incognito mode, which gives you another option of avoiding pages being added to the Recently Closed list. New Incognito windows can be opened from the Chrome menu.