SO jQuery Fiddle

Test Fiddle mainly for SO Questions jQuery 1.4.3, UI 1.8.5

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.5/themes/ui-lightness/jquery-ui.css">
<div class="facebookLike">
    <iframe src="//www.facebook.com/plugins/like.php?href=http%3A%2F%2Fwww.facebook.com%2Fcsuvolleyball&amp;send=false&amp;layout=button_count&amp;width=80&amp;show_faces=false&amp;action=like&amp;colorscheme=light&amp;font&amp;height=21&amp;appId=150920871613500" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:80px; height:21px;" allowTransparency="true"></iframe>
</div>
<div class="facebookLike">
    <iframe src="//www.facebook.com/plugins/like.php?href=http%3A%2F%2Fwww.facebook.com%2Fcsurams&amp;send=false&amp;layout=button_count&amp;width=80&amp;show_faces=false&amp;action=like&amp;colorscheme=light&amp;font&amp;height=21&amp;appId=150920871613500" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:80px; height:21px;" allowTransparency="true"></iframe>
</div>
<div class="facebookLike">
    <iframe src="//www.facebook.com/plugins/like.php?href=http%3A%2F%2Fwww.facebook.com%2FCoachJimMcElwain&amp;send=false&amp;layout=button_count&amp;width=80&amp;show_faces=false&amp;action=like&amp;colorscheme=light&amp;font&amp;height=21&amp;appId=150920871613500" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:80px; height:21px;" allowTransparency="true"></iframe>
</div>

CSS

.facebookLike {display:none;}

JavaScript

var divs = $("div.facebookLike").get().sort(function() {
    return Math.round(Math.random()) - 0.5; //random so we get the right +/- combo
}).slice(0, 1)
$(divs).appendTo(divs[0].parentNode).show();