Cannot read property 'map' of undefined

First of all, set more safe initial data:

getInitialState : function() {
    return {data: {comments:[]}};
},

And ensure your ajax data.

It should work if you follow above two instructions like Demo.

Updated: you can just wrap the .map block with conditional statement.

if (this.props.data) {
  var commentNodes = this.props.data.map(function (comment){
      return (
        <div>
          <h1>{comment.author}</h1>
        </div>
      );
  });
}

I think you forgot to change

data={this.props.data}

to

data={this.state.data}

in the render function of CommentBox. I did the same mistake when I was following the tutorial. Thus the whole render function should look like

render: function() {
  return (
    <div className="commentBox">
      <h1>Comments</h1>
      <CommentList data={this.state.data} />
      <CommentForm />
    </div>
  );
}

instead of

render: function() {
  return (
    <div className="commentBox">
      <h1>Comments</h1>
      <CommentList data={this.props.data} />
      <CommentForm />
    </div>
  );

You need to put the data before render

Should be like this:

var data = [
  {author: "Pete Hunt", text: "This is one comment"},
  {author: "Jordan Walke", text: "This is *another* comment"}
];

React.render(
  <CommentBox data={data}/>,
  document.getElementById('content')
);

Instead of this:

React.render(
  <CommentBox data={data}/>,
  document.getElementById('content')
);

var data = [
  {author: "Pete Hunt", text: "This is one comment"},
  {author: "Jordan Walke", text: "This is *another* comment"}
];