Is it possible to create static classes in PHP (like in C#)?

I want to create a static class in PHP and have it behave like it does in C#, so

1. Constructor is automatically called on the first call to the class
2. No instantiation required

Something of this sort...

static class Hello {
    private static $greeting = 'Hello';

    private __construct() {
        $greeting .= ' There!';
    }

    public static greet(){
        echo $greeting;
    }
}

Hello::greet(); // Hello There!