NullReferenceException in unit test result

I've just started programming in C# Webforms (previous experience in VB Webforms) and I am producing a web app that will be a small part of a bigger project.

I have created 3 separate projects, one for the webforms, one for the class library and one for the tests.

I have added all the projects into one solution and added appropriate references, Both the Webforms and Tests projects reference the class library.

I have a class in the class library that finds the username of the logged in user:

public class LoggedInUser
{
    public string UserName 
    {
        get { return HttpContext.Current.User.Identity.Name; } 
    }

}

In the page load event of one of my pages, I use this class to set the text property of a literal to display the name on the screen.

    protected void Page_Load(object sender, EventArgs e)
    {
        LoggedInUser CurrentUser = new LoggedInUser();
        LitUser.Text = string.Format(" {0}", CurrentUser.UserName);
    }

This works fine.

To be complete I thought I would write a unit test to make sure the logged in username is what I expected.

    [TestMethod]
    public void Test_Logged_In_User_Name()
    {
        LoggedInUser actualUser = new LoggedInUser();
        string expectedUserName = "myUserName";
        string actualUserName = actualUser.UserName;
        Assert.AreEqual(expectedUserName, actualUserName);
    }

When I run the test it throws the following exception:

System.NullReferenceException: Object reference not set to an instance of an object

on this line:

get { return HttpContext.Current.User.Identity.Name; }

Any thoughts would as always be greatly appreciated.