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Is there something similar for Chrome?

There's a setting for both 'Keep local data only until you quit your browser' and 'Block sites from setting any data' under Cookies in stock Chrome.

I don't use it though, so not sure of the effectiveness.

Not exactly. You have to quit the browser. Using this FF extension, you just have to close a tab. So there's no such option available in Chrome.

If you care about privacy don't use a closed source browser especially not from Google...

I use Chromium. As it happens, Chromium and Chrome have the same extension system. Thanks for your half-arsed "concerns", though.