Dreamchaser, I'm using the most recent version of Google Chrome on my iMac. I tried this and it did remove the list of recently closed tabs:
At the top of the screen in Chrome you should see, reading from the far left corner, Chrome, File, Edit, View, History (I’m guessing it’s under "History" that you’re seeing the closed tabs -- if not, please tell us where you're seeing them), Bookmarks, Window, Help.
In the drop-down menu under the word Chrome, choose Clear Browsing Data… (A box will open and you'll see the words “Learn more” toward the bottom of the page. You can click on that if you want to read about the features and choices.)
On the first line, which says, “Obliterate the following items from:” Choose: “From the beginning of time.”
Place a checkmark by Browsing History, Download History, Cookies and other site and plug-in data, Cached images and files, and Hosted app data.
Click “Clear browsing data.”
If that didn’t work, at the bottom of the Clear Browsing Data, where it says: “Saved content settings and search engines will not be cleared and may reflect your browsing habits,” click on the words “content settings” to see if you need to change anything there to customize your browsing privacy to suit your needs.
Few things reveal your intellect and your generosity of spirit—the parallel powers of your heart and mind—better than how you give feedback.~Maria Popova