WPF datagrid IsReadOnly exception

I have a datagrid where i have added a Checkbox column. I want the entire datagrid to be IsReadOnly except the Checkbox column. I have tried:

  <DataGrid x:Name="DataGridView_Customer_Information" HorizontalAlignment="Left" Margin="10,200,0,0" VerticalAlignment="Top" Height="410" Width="697" CanUserAddRows="False" IsReadOnly="True" >
        <DataGrid.Columns>
            <DataGridCheckBoxColumn x:Name="CheckBoxSelectRow" IsReadOnly="False"/>
        </DataGrid.Columns>
    </DataGrid>

But i can imagine that <DataGridCheckBoxColumn x:Name="CheckBoxSelectRow" IsReadOnly="False"/> is overruled by the previous statement. Since its only one column that needs to be able to allow edit (allow to checkmark the checkbox) is it possible to make an expection in the IsReadOnly?

Thanks in advanced