Error rendering react component using Typescript and WebPack

I am trying to build the simplest react component. It just renders a Hello page, but i am getting an Error in my console. I am using typescript as my compiler. I am trying to follow this guide to get the setup for my project: https://github.com/Microsoft/TypeScript-React-Starter

Error

Uncaught ReferenceError: React is not defined
    at Object.<anonymous> (external "React":1)
    at __webpack_require__ (bootstrap 2fd03459d628585593a4:19)
    at Object.module.exports (index.tsx:1)
    at __webpack_require__ (bootstrap 2fd03459d628585593a4:19)
    at Object.<anonymous> (bundle.js:3669)
    at __webpack_require__ (bootstrap 2fd03459d628585593a4:19)
    at module.exports.ctor.super_ (bootstrap 2fd03459d628585593a4:62)
    at bootstrap 2fd03459d628585593a4:62

Here is my WebPack config:

module.exports = {
    entry: "./src/index.tsx",
    output: {
        filename: "bundle.js",
        path: __dirname + "/dist",
        publicPath: "/dist/"
    },

    // Enable sourcemaps for debugging webpack's output.
    devtool: "source-map",

    devServer: {
        headers: {
            'Access-Control-Allow-Origin': '*'
        },
        port: 8282
    },

    resolve: {
        // Add '.ts' and '.tsx' as resolvable extensions.
        extensions: [".ts", ".tsx", ".js", ".json"]
    },

    module: {
        rules: [
            // All files with a '.ts' or '.tsx' extension will be handled by 'awesome-typescript-loader'.
            { test: /\.tsx?$/, loader: "awesome-typescript-loader" },

            // All output '.js' files will have any sourcemaps re-processed by 'source-map-loader'.
            { enforce: "pre", test: /\.js$/, loader: "source-map-loader" }
        ]
    },

    // When importing a module whose path matches one of the following, just
    // assume a corresponding global variable exists and use that instead.
    // This is important because it allows us to avoid bundling all of our
    // dependencies, which allows browsers to cache those libraries between builds.
    externals: {
        "react": "React",
        "react-dom": "ReactDOM"
    },
};

Here is myindex.tsx

import * as React from "react";
import * as ReactDOM from "react-dom";

import { Hello } from "./components/Hello";

ReactDOM.render(
    <Hello compiler="TypeScript" framework="React" />,
    document.getElementById("example")
);

And here is my hello component

import * as React from "react";

export interface HelloProps { compiler: string; framework: string; }

// 'HelloProps' describes the shape of props.
// State is never set so we use the 'undefined' type.
export class Hello extends React.Component<HelloProps, undefined> {
    componentWillMount () {
        if ('pluginLoaded' in window) {
            (window as any).pluginLoaded('hello', function (port: any, context: any) {
                // Future work should interact with the message channel here
            });
        }
    }

    render() {
        return <h1>Hello from {this.props.compiler} and {this.props.framework}!</h1>;
    }
}