Google Maps API throws "Uncaught ReferenceError: google is not defined" only when using AJAX

The API can't be loaded after the document has finished loading by default, you'll need to load it asynchronous.

modify the page with the map:

<div id="map_canvas" style="height: 354px; width:713px;"></div>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script src="https://maps.googleapis.com/maps/api/js?v=3.exp&sensor=false&callback=initialize"></script>
<script>
var directionsDisplay,
    directionsService,
    map;

function initialize() {
  var directionsService = new google.maps.DirectionsService();
  directionsDisplay = new google.maps.DirectionsRenderer();
  var chicago = new google.maps.LatLng(41.850033, -87.6500523);
  var mapOptions = { zoom:7, mapTypeId: google.maps.MapTypeId.ROADMAP, center: chicago }
  map = new google.maps.Map(document.getElementById("map_canvas"), mapOptions);
  directionsDisplay.setMap(map);
}

</script>

For more details take a look at: https://stackoverflow.com/questions/14184956/async-google-maps-api-v3-undefined-is-not-a-function/14185834#14185834

Example: http://jsfiddle.net/doktormolle/zJ5em/

I know this answer is not directly related to this questions' issue but in some cases the "Uncaught ReferenceError: google is not defined" issue will occur if your js file is being called prior to the google maps api you're using...so DON'T DO this:

<script type ="text/javascript" src ="SomeJScriptfile.js"></script>
<script type="text/javascript" src="https://maps.googleapis.com/maps/api/js?v=3.exp"></script>

At a guess, you're initialising something before your initialize function: var directionsService = new google.maps.DirectionsService();

Move that into the function, so it won't try and execute it before the page is loaded.

var directionsDisplay, directionsService;
var map;
function initialize() {
  directionsService = new google.maps.DirectionsService();
  directionsDisplay = new google.maps.DirectionsRenderer();