CanScrollHorizontally shouldn't be an attached property.

src/Perspex.Controls/Presenters/ScrollContentPresenter.cs

@@ -45,7 +45,7 @@ namespace Perspex.Controls.Presenters
         /// Defines the <see cref="CanScrollHorizontally"/> property.
         /// </summary>
         public static readonly StyledProperty<bool> CanScrollHorizontallyProperty =
-            PerspexProperty.Register<ScrollContentPresenter, bool>("CanScrollHorizontally", true);
+            ScrollViewer.CanScrollHorizontallyProperty.AddOwner<ScrollContentPresenter>();
 
         private Size _extent;
         private Size _measuredExtent;

src/Perspex.Controls/ScrollViewer.cs

@@ -17,8 +17,8 @@ namespace Perspex.Controls
         /// <summary>
         /// Defines the <see cref="CanScrollHorizontally"/> property.
         /// </summary>
-        public static readonly AttachedProperty<bool> CanScrollHorizontallyProperty =
-            PerspexProperty.RegisterAttached<ScrollViewer, Control, bool>(nameof(CanScrollHorizontally), true);
+        public static readonly StyledProperty<bool> CanScrollHorizontallyProperty =
+            PerspexProperty.Register<ScrollViewer, bool>(nameof(CanScrollHorizontally), true);
 
         /// <summary>
         /// Defines the <see cref="Extent"/> property.

src/Perspex.Controls/TextBox.cs

@@ -26,6 +26,9 @@ namespace Perspex.Controls
         public static readonly StyledProperty<bool> AcceptsTabProperty =
             PerspexProperty.Register<TextBox, bool>("AcceptsTab");
 
+        public static readonly DirectProperty<TextBox, bool> CanScrollHorizontallyProperty =
+            PerspexProperty.RegisterDirect<TextBox, bool>("CanScrollHorizontally", o => o.CanScrollHorizontally);
+
         // TODO: Should CaretIndex, SelectionStart/End and Text be direct properties?
         public static readonly StyledProperty<int> CaretIndexProperty =
             PerspexProperty.Register<TextBox, int>("CaretIndex", validate: ValidateCaretIndex);
@@ -68,6 +71,7 @@ namespace Perspex.Controls
             public bool Equals(UndoRedoState other) => ReferenceEquals(Text, other.Text) || Equals(Text, other.Text);
         }
 
+        private bool _canScrollHorizontally;
         private TextPresenter _presenter;
         private UndoRedoHelper<UndoRedoState> _undoRedoHelper;
 
@@ -80,12 +84,8 @@ namespace Perspex.Controls
         public TextBox()
         {
             var canScrollHorizontally = this.GetObservable(TextWrappingProperty)
-                .Select(x => x == TextWrapping.NoWrap);
-
-            Bind(
-                ScrollViewer.CanScrollHorizontallyProperty,
-                canScrollHorizontally,
-                BindingPriority.Style);
+                .Select(x => x == TextWrapping.NoWrap)
+                .Subscribe(x => CanScrollHorizontally = x);
 
             var horizontalScrollBarVisibility = this.GetObservable(AcceptsReturnProperty)
                 .Select(x => x ? ScrollBarVisibility.Auto : ScrollBarVisibility.Hidden);
@@ -109,6 +109,12 @@ namespace Perspex.Controls
             set { SetValue(AcceptsTabProperty, value); }
         }
 
+        public bool CanScrollHorizontally
+        {
+            get { return _canScrollHorizontally; }
+            private set { SetAndRaise(CanScrollHorizontallyProperty, ref _canScrollHorizontally, value); }
+        }
+
         public int CaretIndex
         {
             get { return GetValue(CaretIndexProperty); }

src/Perspex.Themes.Default/TextBox.xaml

@@ -28,7 +28,7 @@
               </TextBlock.IsVisible>
             </TextBlock>
             
-            <ScrollViewer CanScrollHorizontally="{TemplateBinding (ScrollViewer.CanScrollHorizontally)}"
+            <ScrollViewer CanScrollHorizontally="{TemplateBinding CanScrollHorizontally}"
                           HorizontalScrollBarVisibility="{TemplateBinding (ScrollViewer.HorizontalScrollBarVisibility)}"
                           VerticalScrollBarVisibility="{TemplateBinding (ScrollViewer.VerticalScrollBarVisibility)}">
               <Panel>