You could scroll to a specific item by using ScrollIntoView() on the ListBox and passing it the newly added item. Depending on your underlying collection, you could for example use the CollectionChanged event to in the handler, scroll to the newly added item there:
People.CollectionChanged += new NotifyCollectionChangedEventHandler( People_CollectionChanged );
void People_CollectionChanged( object sender, NotifyCollectionChangedEventArgs e )
if( e.Action == NotifyCollectionChangedAction.Add )
listbox.ScrollIntoView( e.NewItems[ 0 ] );
Also find attached a basic sample that demonstrates this.
Xceed Software inc.