A 'Binding' can only be set on a DependencyProperty of a DependencyObject

From a custom control based on TextBox, I created a property named Items, in this way:

public class NewTextBox : TextBox
{
    public ItemCollection Items { get; set; }
}

When using the custom control in XAML, I cannot bind the property because it raises exception "A 'Binding' can only be set on a DependencyProperty of a DependencyObject.".

How do I solve this exception?