DataGridView with a checkbox with default value checked

I think there is no way of setting the checked value on column declaration. You will have to iterate through the rows checking it after datasource is set (for example in DataBindingComplete event):

for (int i = 0; i < dataGridView1.Rows.Count -1; i++)
{
dataGridView1.Rows[i].Cells[0].Value = true;
}

With your column name:

for (int i = 0; i < dataGridView1.Rows.Count -1; i++)
{
   dataGridView1.Rows[i].Cells["Export"].Value = true;
}

Try to do it like this:

foreach (DataGridViewRow row in dgv.Rows)     
{
    row.Cells[CheckBoxColumn.Name].Value = true;     
}