Trigger AngularJS routing from javascript

I'm trying to write a simple app that incorporates authentication.

var chatApp = angular.module('chat-app', ['ngRoute']);

chatApp.config(['$routeProvider',
    function($routeProvider) {
      $routeProvider.
        when('/chat', {
          templateUrl : 'static/html/partial/chat.html',
          controller: 'chatCtrl'
        });
    }
]);

window.onload = function() {
  checkAuth();
};

function checkAuth() {
  var userId = localStorage.getItem('chat-id');
  var userProfile = localStorage.getItem('chat-profile');

  if(!userId) {
    // Show login dialog and handle authentication
    // This is done for me by an external service (auth0)
    userId, userProfile = authenticate();  // Abstracting away for simplicity
    localStorage.setItem('chat-id', userId);
    localStorage.setItem('chat-profile', JSON.stringify(userProfile));
  }
  else {
    userProfile = JSON.parse(userProfile);
  }
  angular.element($('html')).scope().nickname = userProfile.nickname;
  // Now redirect to /chat
  window.location.href = '#/chat';
}

When I run the above code, I can see that authentication is happening correctly and it executes window.location.href = '#/chat';. However, this does not trigger Angular's routing rules and therefore, it does not load the template that I have defined.

I think once I get hold of the Angular $location object, I can set the URL and hope Angular does the rest. What is the right way to trigger Angular routing from plain javascript?