This cannot be done with CSS alone. try the autogrow jquery plugin.
https://github.com/jaz303/jquery-grab-bag/blob/master/javascripts/jquery.autogrow-textarea.js
You can also see autogrow demo here http://onehackoranother.com/projects/jquery/jquery-grab-bag/autogrow-textarea.html
It's lightweight and easy to use. Here's how it's done. Define your textarea id. Include the jquery js file before