Wpf – Setting Column Background in WPF ListView/Gridview

I'm looking to set the background of a column in a WPF GridView. Many Google results have pointed towards setting the GridViewColumn.CellTemplate to change the appearance of a column. However, I'm met with an issue when setting the background color; it's not stretching to fill the cell:

Here's the xaml I'm working with:

<Window x:Class="ScratchPadWpf.Window1"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  Title="Window1" Width="300" Height="300">
  <Grid>
    <ListView ItemsSource="{Binding}">
      <ListView.View>
        <GridView>
          <GridViewColumn>
            <GridViewColumn.CellTemplate>
              <DataTemplate>
                <Grid Background="Red">
                  <TextBlock Text="{Binding FirstName}"/>
                </Grid>
              </DataTemplate>
            </GridViewColumn.CellTemplate>  
          </GridViewColumn>
          <GridViewColumn>
            <GridViewColumn.CellTemplate>
              <DataTemplate>
                <Grid Background="Yellow">
                  <TextBlock Text="{Binding LastName}"/>
                </Grid>
              </DataTemplate>
            </GridViewColumn.CellTemplate>  
          </GridViewColumn>
        </GridView>
      </ListView.View>
    </ListView>
  </Grid>
</Window>

And the xaml.cs for good measure:

public partial class Window1 : Window
{
  public Window1()
  {
    InitializeComponent();
    DataContext = new[]
    {
      new {FirstName = "Jim", LastName = "Bob"},
      new {FirstName = "Frank", LastName = "Smith"},
      new {FirstName = "Tooth", LastName = "Paste"},
    };
  }
}

Setting the DataTemplate's Grid's width and height to be larger than the cell with a negative margin can produce a close result, but if you resize the column, the problem shows itself again.

<Grid Background="Yellow" Height="22" Width="50" Margin="-6">

Is there a way to fill the cell with color?