Dear Friend,
Try to do it like this:-
dataGridView1.Rows[index].Cells.FormattedValue=1;
As the checkbox value when set then it should be set
TRUE or
False but when you are setting it to 1 it is not able to map the value but by using the FormattedValue, you are actually setting the value of TRUE which is 1.
Don't forget to mark this as your answer if it helps you out.
Thanks