Accessing Apex REST from Site.com

CORS_MessageService.cls

@RestResource(urlMapping='/v1.0/messages')
global class MessageService {
    
    @HttpGet
    global static void getMessages() {

        // buildMessages gets FeedItems
        List<Message> messages = buildMessages();
       
        RestResponse res = RestContext.response;
        res.addHeader('Content-Type', 'application/json');
        res.responseBody = Blob.valueOf( JSON.serialize(messages) );
    }
    
    // build messages implementation...
}

CORS_Site.com_Page_Head_Markup.html

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>

<script>
$(document).ready(function() {    
    $.ajax({
        type: 'GET',
        url: '{!Site.messagesURL}',
        success: function(response) {
            var messageList = $('<ul></ul>');
            $.each(response, function(idx, val) {
            	messageList.append(
                    '<li>' +
                    'Date: ' + val.messageDate + '<br />' +
                    'Title: ' + val.title + '<br />' + 
                    'Body: ' + val.body + '<br />' +
                    '</li>'
               );   
            });
            $('#messages').html(messageList);
    	}
    });
});
</script>

MessageService.cls

@RestResource(urlMapping='/v1.0/messages')
global class MessageService {

    private static final String GROUP_ID = '<insert_your_chatter_groupid>';
    
    @HttpGet
    global static void getMessages() {
        String callback = RestContext.request.params.get('callback');
        
        // buildMessages gets FeedItems
        List<Message> messages = buildMessages();
       
        RestResponse res = RestContext.response;
        
        // add in a CORS header response
       // res.addHeader('Access-Control-Allow-Origin','https://sitepreview.gus.force.com');
        res.addHeader('Access-Control-Allow-Origin','https://myown-developer-edition.gus.force.com');
        
        res.addHeader('Content-Type', 'application/javascript');
        res.responseBody = Blob.valueOf(callback + '(' + JSON.serialize(messages) + ')');
        
    }
    
    private static List<Message> buildMessages() {
        List<Message> messages = new List<Message>();
        
        for (FeedItem item : [
            SELECT Title, Body, CreatedDate
            FROM FeedItem
            WHERE ParentId = :GROUP_ID
            ORDER BY CreatedDate DESC
            Limit 5
        ]) {
            messages.add(new Message(item.CreatedDate.date(), item.Title, item.Body));
        }
        return messages;
    }
    
    class Message { 
        public Message(Date d, String t, String b) {
            messageDate = d;
            title = t;
            body = b;
        }
        
        public Date messageDate { get; set; }
        public String title { get; set; }
        public String body { get; set; }
    }
}

Site.com_Page_Head_Markup.html

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>

<script>
$(document).ready(function() {    
    $.ajax({
        type: 'GET',
        url: '{!Site.messagesURL}',
  	dataType: 'jsonp',
	success: function(response) {
            var messageList = $('<ul></ul>');
            $.each(response, function(idx, val) {
            	messageList.append(
                    '<li>' +
                    'Date: ' + val.messageDate + '<br />' +
                    'Title: ' + val.title + '<br />' + 
                    'Body: ' + val.body + '<br />' +
                    '</li>'
               );   
            });
            $('#messages').html(messageList);
    	}
    });
});
</script>