public class ViewModel
    {
        public string HelloText { get { return "Привет"; } }
    }

    public class Attached : DependencyObject
    {
        public static readonly DependencyProperty ServiceProperty = DependencyProperty.RegisterAttached("Service", typeof(string), typeof(UIElement), new PropertyMetadata(null, (d, e) =>
        {
            
        }));

        public static void SetService(UIElement obj, string value) { obj.SetValue(ServiceProperty, value); }
        public static string GetService(UIElement obj) { return (string)obj.GetValue(ServiceProperty); }
     }

<TextBox Height="57" HorizontalAlignment="Left" Margin="106,96,0,0" Name="textBox1" VerticalAlignment="Top" Width="202" local:Attached.Service="{Binding HelloText, Mode=OneWay}"/>