Error : 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>
      );
  });
}