How do I add classNames to the first element of the page without using a view?

@BenediktD, I usually handle this by adding a <div> in the index.html and binding it in the rootElement on Ember.Application.create().

<body>
<div id="my-ember-app" class="wrapper"></div>
</body>
Ember.Application.create({
  rootElement: '#my-ember-app'
});

Unless you are trying to avoid touching your index.html or have another use for view/application.js; this should be better and you are saving yourself an extra Ember.Component / Ember.View layer that you need to go through.