Assign a single handler to the button click (MouseEvent.CLICK is the right event to use) and check the field is populated in the handler:
function clickButtonHandler(event:MouseEvent):void
{
var message:Object = new Object();
// Check the field is populated
if (txtUser.text != "")
{
message.text = txtMessage.text;
message.userName = txtUser.text;
showMessage(message);
//Posts to ALL OTHER swf files..
group.post(message);
}
else
{
// Nothing in the input field, show the alert
showAlert();
}
}
function showMessage(message:Object):void
{
output_txt.appendText(message.userName+": "+message.text + "\n");
}
function showAlert():void
{
var alert:URLRequest = new URLRequest("javascript:alert('Please enter your User name')");
navigateToURL(alert, "_self");
}