I don't think I need to explain why you might want to do this.

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@-moz-document domain("youtube.com")
{
    div#watch-discussion {
        display: none;
    }
}

Add to userContent.css if you use Firefox. Strip off the outer block and add elsewhere if you do not use Firefox.

If you prefer a more flexible solution, there is a Greasemonkey script in misc.