public partial class home : System.Web.UI.Page
{
    protected void Page_Load(object sender, EventArgs e)
    {

    }
    private string chatitems
    {
        get
        {
            if(Application["un"]==null)
                Application["un"] = "";
            return Application["un"].ToString();
        }
        set
        {
            Application["un"] = value;
        }
    }
    protected void Timer1_Tick(object sender, EventArgs e)
    {
        Label1.Text = chatitems;
    }
    protected void Button1_Click(object sender, EventArgs e)
    {
        chatitems = txt.Text + "<br />" + chatitems;
    }
}

<input id="submitButton" type="submit" value="Submit"/>

</body>

<script type="text/javascript">
    // select the button element
    var button = document.getElementById('submitButton');
    // add an event listener for the on click event.
    button.AddEventListener("onClick", function(){
        var txt = document.getElementById('<%=txt.ClientId%>');
        // I suppose that you will define the chatitems somewhere above, because I don't //get its use, reading your code.
        chatitems += txt.val()+"<br/>";
    });
</script>