Not sure why it didn't work, but this should. You need to place it at the page body instead of the head.
Code:
<script>
if(navigator.userAgent.indexOf('Chrome')>=0){
 document.getElementsByClassName("parallax")[0].style.willChange="transform";
 document.getElementsByClassName("parallax2")[0].style.willChange="transform";
}
</script>
If you consider to use it I recommend you try it on older versions of Chrome too before uploading to your site.