How to get a ListBox ItemTemplate to stretch horizontally the full width of the ListBox?

I want to have the ListItems to extend with their orange background the full width of the Listbox.

Currently they are only as wide as the FirstName + LastName.

I've set every element I can to: HorizontalAlignment="Stretch".

I want the background of the ListboxItems to expand as the user stretches the Listbox so I don't want to put in absolute values.

What do I have to do so that the background color of the ListBoxItems fill the width of the ListBox?

<Window x:Class="TestListBoxSelectedItemStyle.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="clr-namespace:TestListBoxSelectedItemStyle"
    Title="Window1" Height="300" Width="300">

    <Window.Resources>
        <local:CustomerViewModel x:Key="TheDataProvider"/>

        <DataTemplate x:Key="CustomerItemTemplate">
            <Border CornerRadius="5" Background="Orange" HorizontalAlignment="Stretch" Padding="5" Margin="3">
                <StackPanel Orientation="Horizontal" HorizontalAlignment="Stretch" Width="Auto">
                    <TextBlock HorizontalAlignment="Stretch">
                    <TextBlock.Text>
                        <MultiBinding StringFormat="{}{0} {1}">
                            <Binding Path="FirstName"/>
                            <Binding Path="LastName"/>
                        </MultiBinding>
                    </TextBlock.Text>
                    </TextBlock>
                </StackPanel>
            </Border>
        </DataTemplate>

    </Window.Resources>

    <Grid>
        <ListBox ItemsSource="{Binding Path=GetAllCustomers, Source={StaticResource TheDataProvider}}"
                 ItemTemplate="{StaticResource CustomerItemTemplate}"/>
    </Grid>
</Window>