public class CustomChat : RadChat
{
    private ScrollViewer scrollViewer;

    internal ScrollViewer ScrollViewer
    {
        get
        {
            if (this.scrollViewer == null)
            {
                this.scrollViewer = this.ChildrenOfType<ScrollViewer>().Where(sc => sc.Name == "PART_ScrollViewer").FirstOrDefault();
            }

            return this.scrollViewer;
        }
    }

    protected override void OnPointerWheelChanged(PointerRoutedEventArgs e)
    {
        if (this.ScrollViewer != null)
        {
            int delta = e.GetCurrentPoint(this).Properties.MouseWheelDelta;
            double wheelDetents = delta / 120.0;
            double scrollableRange = ScrollViewer.ExtentHeight - ScrollViewer.ViewportHeight;                
            double step = 0.01 * scrollableRange;
            double offsetDelta = wheelDetents * step;
            double newOffset = ScrollViewer.VerticalOffset - offsetDelta;
            newOffset = Math.Max(0, Math.Min(ScrollViewer.ExtentHeight, newOffset));

            ScrollViewer.ScrollToVerticalOffset(newOffset);
        }
    }
}