gistfile1.js

var Component = React.createClass({
    render: function() {
        return (
            <div className="Component">
                // More content here
            </div>
        )
    }
});

var ComponentList = React.createClass({
    render: function() {
        return (
            // What I'd like is to be able to add to the Component
            // classnames from here so the classnames end up mixed together
            <Component className="Component--wide" />
            <Component className="Component--evenWider u-someUtility" />
            <Component />
        )
    }
})

// Desired output
<div class="Component Component--wide"></div> // etc