Edit in JSFiddle

Result
JavaScript 1.7
HTML

/** @jsx React.DOM */
/* global React, Backbone, $ */

var MyWidget = React.createClass({
  render: function() {
    return (
      <a href="#" onClick={this.props.handleClick}>Do something!</a>
    );
  }
});

var MyView = Backbone.View.extend({
  el: 'body',
  template: '<div class="widget-container"></div>' +
            '<div class="outside-container"></div>',
  render: function() {
    this.$el.html(this.template);

    React.renderComponent(new MyWidget({
      handleClick: this.clickHandler.bind(this)
    }), this.$('.widget-container').get(0));

    return this;
  },
  clickHandler: function() {
    this.$(".outside-container").html("The link was clicked!");
  }
});

new MyView().render();

<script src="http://fb.me/react-js-fiddle-integration.js"></script>

<body>
</body>