Workaround:
this.radChat1.ChatElement.InputTextBox.TextBoxItem.TextBoxControl.Multiline = true;
this.radChat1.ChatElement.InputTextBox.ButtonsStack.Children.Remove(this.radChat1.ChatElement.ShowToolbarButtonElement);
this.radChat1.ChatElement.InputTextBox.ButtonsStack.Children.Remove(this.radChat1.ChatElement.SendButtonElement);
StackLayoutElement stack = new StackLayoutElement();
stack.MinSize = new Size(0, 60);
this.radChat1.ChatElement.InputTextBox.Parent.Children.Add(stack);
this.radChat1.ChatElement.InputTextBox.Parent.Children.Remove(this.radChat1.ChatElement.InputTextBox);
stack.StretchHorizontally = true;
stack.Orientation = Orientation.Horizontal;
stack.Children.Add(this.radChat1.ChatElement.InputTextBox);
stack.Children.Add(this.radChat1.ChatElement.ShowToolbarButtonElement);
stack.Children.Add(this.radChat1.ChatElement.SendButtonElement);
this.radChat1.ChatElement.ShowToolbarButtonElement.StretchHorizontally = false;
this.radChat1.ChatElement.SendButtonElement.StretchHorizontally = false;