facebookmessenger.html

<script>
  function OpenInNewTab() {
    var screenwidth = screen.width-500;
    window.open("http://m.me/fiercelycurious", '_blank',"width=500,height=800,left="+screenwidth);
  }
</script>


<a href="http://m.me/fiercelycurious" target="_blank" onclick="OpenInNewTab();"> <!-- m.me/facebookpage works for any facebook page -->
  <div class="fbmessenger">
  <img src="https://lh5.ggpht.com/0VYAvZLR9YhosF-thqm8xl8EWsCfrEY_uk2og2f59K8IOx5TfPsXjFVwxaHVnUbuEjc=w300" /> <!-- I host the file directly but I'm hotlinking from the Google Play store here for the png file -->
  <span class="tooltiptext mobilehidden">Message Us</span>
  </div>
  </a>

For more context, see here: http://tomcritchlow.com/2016/05/10/facebook-livechat/

Awesome and simples solution. Thanks