Social interaction of your customers are very important to analyze their impact on your conversions.
Reading the official Google Analytics developers guide, the solution seems to be the usage of the following code:

FB.Event.subscribe('edge.create', function(targetUrl)
{
    _gaq.push(['_trackSocial', 'facebook', 'like', targetUrl]);
});

Unfortunately this code doesn't work if you are correctly loading the Facebook SDK asynchronously, that's because may be the the SDK is still loading when you subscribe to the event.

<div id="fb-root"></div>
<script>
    window.fbAsyncInit = function()
    {
        // init the FB JS SDK
        FB.init(
        {
            appId : 'YOUR_APP_ID',
            channelUrl : '//WWW.YOUR_DOMAIN.COM',
            status : true,
            cookie : true,
            xfbml : true
        });

        // Add event subscripion here
        FB.Event.subscribe('edge.create', function (targetUrl)
        {
            _gaq.push(['_trackSocial','facebook', 'like', targetUrl]);
        });
    };

    // Load the SDK's source Asynchronously
    (function(d)
    {
        var js, id = 'facebook-jssdk', ref = d.getElementsByTagName('script')[0];
        if (d.getElementById(id)) {return;}
        js = d.createElement('script'); js.id = id; js.async = true;
        js.src = "//connect.facebook.net/en_US/all.js";
        ref.parentNode.insertBefore(js, ref);
    }(document));
</script>

If you want to add the event handler programmatically, the correct solution is to use the window.fbAsyncInit event to append the like event subscription to the Facebook SDK initialization.
In the following code I used jQuery to append the event subscription after DOM initialization.

$ (function ()
{
    var exsistingFbAsyncInit = window.fbAsyncInit;
    if (exsistingFbAsyncInit == null)
        window.fbAsyncInit = function ()
        {
            FB.Event.subscribe('edge.create', function (targetUrl)
            {
                _gaq.push(['_trackSocial','facebook', 'like', targetUrl]);
            });
        };
    else
        window.fbAsyncInit = function ()
        {
            exsistingFbAsyncInit();
            FB.Event.subscribe('edge.create', function (targetUrl)
            {
                _gaq.push(['_trackSocial','facebook', 'like', targetUrl]);
            });
        };
});