Google doesn’t offer a way to hide it but you can get rid of the obnoxious gratuitous fluff with a custom user stylesheet.

On a Mac, this is where to put the style rules:
~/Library/Application Support/Google/Chrome/Default/User StyleSheets/Custom.css

You can use a text editor to get it in there or do something like:
cat > ~/Library/Application\ Support/Google/Chrome/Default/User\ StyleSheets/Custom.css <<EOT
#card-slider-frame,
#recently-closed-menu-button,
#dot-list {
display: none !important;
}
EOT

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